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Scientia Fellow (Level C)

Dr Chris Goodrich

  • PhD Mathematics (University of Nebraska-Lincoln)
Science
School of Mathematics & Statistics
Phone
9385 7036
E-mail
c.goodrich@unsw.edu.au
Location
School of Mathematics and Statistics UNSW Sydney NSW 2052 The Red Centre Room 2070
  • Books | 2016
    2016, Discrete fractional calculus, http://dx.doi.org/10.1007/978-3-319-25562-0
  • Journal articles | 2023
    2023, 'A Study of Monotonicity Analysis for the Delta and Nabla Discrete Fractional Operators of the Liouville–Caputo Family', Axioms, 12, http://dx.doi.org/10.3390/axioms12020114
    Journal articles | 2023
    2023, 'Analytical and numerical negative boundedness of fractional differences with Mittag–Leffler kernel', AIMS Mathematics, 8, pp. 5540 - 5550, http://dx.doi.org/10.3934/math.2023279
    Journal articles | 2023
    2023, 'Nonlocal differential equations with convex convolution coefficients', Journal of Fixed Point Theory and Applications, 25, http://dx.doi.org/10.1007/s11784-022-01008-w
    Journal articles | 2023
    2023, 'Nonlocal differential equations with (p,q) growth', Bulletin of the London Mathematical Society, http://dx.doi.org/10.1112/blms.12798
    Journal articles | 2023
    2023, 'Some new parameterized Newton-type inequalities for differentiable functions via fractional integrals', Journal of Inequalities and Applications, 2023, http://dx.doi.org/10.1186/s13660-023-02953-x
    Journal articles | 2022
    2022, 'An analysis of nonlocal difference equations with finite convolution coefficients', Journal of Fixed Point Theory and Applications, 24, http://dx.doi.org/10.1007/s11784-021-00914-9
    Journal articles | 2022
    2022, 'Existence and monotonicity of nonlocal boundary value problems: The one-dimensional case', Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 152, pp. 1 - 27, http://dx.doi.org/10.1017/prm.2020.90
    Journal articles | 2022
    2022, 'NONEXISTENCE AND PARAMETER RANGE ESTIMATES FOR CONVOLUTION DIFFERENTIAL EQUATIONS', Proceedings of the American Mathematical Society, Series B, 9, pp. 254 - 265, http://dx.doi.org/10.1090/bproc/130
    Journal articles | 2022
    2022, 'New classifications of monotonicity investigation for discrete operators with Mittag-Leffler kernel', Mathematical Biosciences and Engineering, 19, pp. 4062 - 4074, http://dx.doi.org/10.3934/mbe.2022186
    Journal articles | 2022
    2022, 'On positivity and monotonicity analysis for discrete fractional operators with discrete Mittag–Leffler kernel', Mathematical Methods in the Applied Sciences, 45, pp. 6391 - 6410, http://dx.doi.org/10.1002/mma.8176
    Journal articles | 2022
    2022, 'Partial regularity for minimizers of discontinuous quasiconvex integrals with general growth', Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 152, pp. 1191 - 1232, http://dx.doi.org/10.1017/prm.2021.53
    Journal articles | 2022
    2022, 'Partial regularity of minimizers of asymptotically convex functionals with p(x)-growth', STUDIA MATHEMATICA, http://dx.doi.org/10.4064/sm210104
    Journal articles | 2022
    2022, 'Partial regularity of minimizers of asymptotically convex functionals with p(x)-growth', Studia Mathematica, 264, pp. 71 - 102, http://dx.doi.org/10.4064/sm210104-20-9
    Journal articles | 2021
    2021, 'A one-dimensional Kirchhoff equation with generalized convolution coefficients', Journal of Fixed Point Theory and Applications, 23, http://dx.doi.org/10.1007/s11784-021-00910-z
    Journal articles | 2021
    2021, 'A topological approach to a class of one-dimensional Kirchhoff equations', Proceedings of the American Mathematical Society, Series B, 8, pp. 158 - 172, http://dx.doi.org/10.1090/bproc/84
    Journal articles | 2021
    2021, 'A topological approach to nonlocal elliptic partial differential equations on an annulus', Mathematische Nachrichten, 294, pp. 286 - 309, http://dx.doi.org/10.1002/mana.201900204
    Journal articles | 2021
    2021, 'ANALYSIS OF CONVEXITY RESULTS FOR DISCRETE FRACTIONAL NABLA OPERATORS', Rocky Mountain Journal of Mathematics, 51, pp. 1981 - 2001, http://dx.doi.org/10.1216/rmj.2021.51.1981
    Journal articles | 2021
    2021, 'ANALYTICAL and NUMERICAL MONOTONICITY RESULTS for DISCRETE FRACTIONAL SEQUENTIAL DIFFERENCES with NEGATIVE LOWER BOUND', Communications on Pure and Applied Analysis, 20, pp. 339 - 358, http://dx.doi.org/10.3934/cpaa.2020269
    Journal articles | 2021
    2021, 'An analysis of polynomial sequences and their application to discrete fractional operators', Journal of Difference Equations and Applications, 27, pp. 1081 - 1102, http://dx.doi.org/10.1080/10236198.2021.1965132
    Journal articles | 2021
    2021, 'Analytical and numerical convexity results for discrete fractional sequential differences with negative lower bound', Journal of Difference Equations and Applications, 27, pp. 317 - 341, http://dx.doi.org/10.1080/10236198.2021.1894142
    Journal articles | 2021
    2021, 'Convexity, monotonicity, and positivity results for sequential fractional nabla difference operators with discrete exponential kernels', Mathematical Methods in the Applied Sciences, 44, pp. 7099 - 7120, http://dx.doi.org/10.1002/mma.7247
    Journal articles | 2021
    2021, 'Differential equations with multiple sign changing convolution coefficients', International Journal of Mathematics, 32, http://dx.doi.org/10.1142/S0129167X21500579
    Journal articles | 2021
    2021, 'Discrete Kirchhoff equations with sign-changing coefficients', Journal of Difference Equations and Applications, 27, pp. 664 - 685, http://dx.doi.org/10.1080/10236198.2021.1929945
    Journal articles | 2021
    2021, 'Monotonicity results for CFC nabla fractional differences with negative lower bound', Analysis (Germany), 41, pp. 221 - 229, http://dx.doi.org/10.1515/anly-2021-0011
    Journal articles | 2021
    2021, 'Monotonicity results for sequential fractional differences of mixed orders with negative lower bound', Journal of Difference Equations and Applications, 27, pp. 1574 - 1593, http://dx.doi.org/10.1080/10236198.2021.1999434
    Journal articles | 2021
    2021, 'Nonlocal Differential Equations with Convolution Coefficients and Applications to Fractional Calculus', Advanced Nonlinear Studies, 21, pp. 767 - 787, http://dx.doi.org/10.1515/ans-2021-2145
    Journal articles | 2021
    2021, 'Nonlocal differential equations with concave coefficients of convolution type', Nonlinear Analysis, Theory, Methods and Applications, 211, http://dx.doi.org/10.1016/j.na.2021.112437
    Journal articles | 2021
    2021, 'Partial regularity of minimizers of asymptotically convex functionals with Morrey coefficients', Journal of Mathematical Analysis and Applications, 498, http://dx.doi.org/10.1016/j.jmaa.2021.124962
    Journal articles | 2021
    2021, 'Theoretical and numerical analysis of monotonicity results for fractional difference operators', Applied Mathematics Letters, 117, http://dx.doi.org/10.1016/j.aml.2021.107104
    Journal articles | 2021
    2021, 'Topological analysis of doubly nonlocal boundary value problems', Journal of Fixed Point Theory and Applications, 23, http://dx.doi.org/10.1007/s11784-021-00865-1
    Journal articles | 2020
    2020, 'A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity', Israel Journal of Mathematics, 236, pp. 533 - 589, http://dx.doi.org/10.1007/s11856-020-1991-2
    Journal articles | 2020
    2020, 'Nonlocal difference equations with sign-changing coefficients', Applied Mathematics Letters, 106, http://dx.doi.org/10.1016/j.aml.2020.106371
    Journal articles | 2020
    2020, 'Partial regularity of solutions to p(x)-Laplacian PDEs with discontinuous coefficients', Journal of Differential Equations, 268, pp. 5440 - 5468, http://dx.doi.org/10.1016/j.jde.2019.11.026
    Journal articles | 2020
    2020, 'Pointwise conditions for perturbed Hammerstein integral equations with monotone nonlinear, nonlocal elements', Banach Journal of Mathematical Analysis, 14, pp. 290 - 312, http://dx.doi.org/10.1007/s43037-019-00017-1
    Journal articles | 2020
    2020, 'Positivity and monotonicity results for triple sequential fractional differences via convolution', Analysis (Germany), 40, pp. 89 - 103, http://dx.doi.org/10.1515/anly-2019-0050
    Journal articles | 2020
    2020, 'Positivity, monotonicity, and convexity for convolution operators', Discrete and Continuous Dynamical Systems- Series A, 40, pp. 4961 - 4983, http://dx.doi.org/10.3934/dcds.2020207
    Journal articles | 2019
    2019, 'A uniformly sharp convexity result for discrete fractional sequential differences', Rocky Mountain Journal of Mathematics, 49, pp. 2571 - 2586, http://dx.doi.org/10.1216/RMJ-2019-49-8-2571
    Journal articles | 2019
    2019, 'An analysis of the sharpness of monotonicity results via homotopy for sequential fractional operators', Applied Mathematics Letters, 98, pp. 446 - 452, http://dx.doi.org/10.1016/j.aml.2019.07.003
    Journal articles | 2019
    2019, 'An application of a nonstandard cone to discrete boundary value problems with unbounded indefinite forcing', Journal of Difference Equations and Applications, 25, pp. 882 - 903, http://dx.doi.org/10.1080/10236198.2019.1639684
    Journal articles | 2019
    2019, 'Coercive functionals and their relationship to multiplicity of solution to nonlocal boundary value problems', Topological Methods in Nonlinear Analysis, 54, pp. 409 - 426, http://dx.doi.org/10.12775/TMNA.2019.029
    Journal articles | 2019
    2019, 'Hölder continuity of weak solutions of p-Laplacian PDEs with VMO coefficients', Nonlinear Analysis, Theory, Methods and Applications, 185, pp. 336 - 355, http://dx.doi.org/10.1016/j.na.2019.03.015
    Journal articles | 2019
    2019, 'Mixed order monotonicity results for sequential fractional nabla differences', Journal of Difference Equations and Applications, 25, pp. 837 - 854, http://dx.doi.org/10.1080/10236198.2018.1561883
    Journal articles | 2019
    2019, 'Operators with gaussian kernel bounds on mixed morrey spaces', Filomat, 33, pp. 5219 - 5230, http://dx.doi.org/10.2298/FIL1916219A
    Journal articles | 2019
    2019, 'Positive solutions for a system of first-order discrete fractional boundary value problems with semipositone nonlinearities', Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 113, pp. 1343 - 1358, http://dx.doi.org/10.1007/s13398-018-0551-7
    Journal articles | 2019
    2019, 'Sharp monotonicity results for fractional nabla sequential differences', Journal of Difference Equations and Applications, 25, pp. 801 - 814, http://dx.doi.org/10.1080/10236198.2018.1542431
    Journal articles | 2018
    2018, 'A general low-order partial regularity theory for asymptotically convex functionals with asymptotic dependence on the minimizer', Calculus of Variations and Partial Differential Equations, 57, http://dx.doi.org/10.1007/s00526-018-1422-y
    Journal articles | 2018
    2018, 'A uniformly sharp monotonicity result for discrete fractional sequential differences', Archiv der Mathematik, 110, pp. 145 - 154, http://dx.doi.org/10.1007/s00013-017-1106-4
    Journal articles | 2018
    2018, 'Monotonicity and non-monotonicity results for sequential fractional delta differences of mixed order', Positivity, 22, pp. 551 - 573, http://dx.doi.org/10.1007/s11117-017-0527-4
    Journal articles | 2018
    2018, 'New Harnack inequalities and existence theorems for radially symmetric solutions of elliptic PDEs with sign changing or vanishing Green's function', Journal of Differential Equations, 264, pp. 236 - 262, http://dx.doi.org/10.1016/j.jde.2017.09.011
    Journal articles | 2018
    2018, 'Partial regularity of minimizers of functionals with discontinuous coefficients of low integrability with applications to nonlinear elliptic systems', Communications in Partial Differential Equations, 43, pp. 1599 - 1626, http://dx.doi.org/10.1080/03605302.2018.1517794
    Journal articles | 2018
    2018, 'Perturbed Integral Operator Equations of Volterra Type with Applications to p -Laplacian Equations', Mediterranean Journal of Mathematics, 15, http://dx.doi.org/10.1007/s00009-018-1090-3
    Journal articles | 2018
    2018, 'Radially symmetric solutions of elliptic PDEs with uniformly negative weight', Annali di Matematica Pura ed Applicata, 197, pp. 1585 - 1611, http://dx.doi.org/10.1007/s10231-018-0738-8
    Journal articles | 2017
    2017, 'A new coercivity condition applied to semipositone integral equations with nonpositive, unbounded nonlinearities and applications to nonlocal BVPs', Journal of Fixed Point Theory and Applications, 19, pp. 1905 - 1938, http://dx.doi.org/10.1007/s11784-016-0340-x
    Journal articles | 2017
    2017, 'A sharp convexity result for sequential fractional delta differences', Journal of Difference Equations and Applications, 23, pp. 1986 - 2003, http://dx.doi.org/10.1080/10236198.2017.1380635
    Journal articles | 2017
    2017, 'An almost sharp monotonicity result for discrete sequential fractional delta differences', Journal of Difference Equations and Applications, 23, pp. 1190 - 1203, http://dx.doi.org/10.1080/10236198.2017.1307351
    Journal articles | 2017
    2017, 'Coercive nonlocal elements in fractional differential equations', Positivity, 21, pp. 377 - 394, http://dx.doi.org/10.1007/s11117-016-0427-z
    Journal articles | 2017
    2017, 'Monotonicity results for delta fractional differences revisited', Mathematica Slovaca, 67, pp. 895 - 906, http://dx.doi.org/10.1515/ms-2017-0018
    Journal articles | 2017
    2017, 'New monotonicity conditions in discrete fractional calculus with applications to extremality conditions', Analysis (Germany), 37, pp. 145 - 156, http://dx.doi.org/10.1515/anly-2016-0039
    Journal articles | 2017
    2017, 'On Semipositone Non-Local Boundary-Value Problems with Nonlinear or Affine Boundary Conditions', Proceedings of the Edinburgh Mathematical Society, 60, pp. 635 - 649, http://dx.doi.org/10.1017/S0013091516000146
    Journal articles | 2017
    2017, 'Partial Lipschitz regularity of minimizers of asymptotically convex functionals with general growth conditions', Journal of Differential Equations, 263, pp. 4400 - 4428, http://dx.doi.org/10.1016/j.jde.2017.05.017
    Journal articles | 2017
    2017, 'Pointwise conditions in discrete boundary value problems with nonlocal boundary conditions', Applied Mathematics Letters, 67, pp. 7 - 15, http://dx.doi.org/10.1016/j.aml.2016.11.011
    Journal articles | 2017
    2017, 'The effect of a nonstandard cone on existence theorem applicability in nonlocal boundary value problems', Journal of Fixed Point Theory and Applications, 19, pp. 2629 - 2646, http://dx.doi.org/10.1007/s11784-017-0448-7
    Journal articles | 2017
    2017, 'The relation between nabla fractional differences and Nabla integer differences', Filomat, 31, pp. 1741 - 1753, http://dx.doi.org/10.2298/FIL1706741B
    Journal articles | 2016
    2016, 'A note on convexity, concavity, and growth conditions in discrete fractional calculus with delta difference', Mathematical Inequalities and Applications, 19, pp. 769 - 779, http://dx.doi.org/10.7153/mia-19-57
    Journal articles | 2016
    2016, 'A note on perturbed Hammerstein equations with applications to nonlocal boundary value problems', Analysis (Germany), 36, pp. 183 - 193, http://dx.doi.org/10.1515/anly-2015-0030
    Journal articles | 2016
    2016, 'Coercivity of linear functionals on finite dimensional spaces and its application to discrete BVPs', Journal of Difference Equations and Applications, 22, pp. 623 - 636, http://dx.doi.org/10.1080/10236198.2015.1125896
    Journal articles | 2016
    2016, 'On partial Hölder continuity and a Caccioppoli inequality for minimizers of asymptotically convex functionals between Riemannian manifolds', Annali di Matematica Pura ed Applicata, 195, pp. 1405 - 1461, http://dx.doi.org/10.1007/s10231-015-0521-z
    Journal articles | 2016
    2016, 'Perturbed hammerstein integral equations with sign-changing kernels and applications to nonlocal boundary value problems and elliptic pdes', Journal of Integral Equations and Applications, 28, pp. 509 - 549, http://dx.doi.org/10.1216/JIE-2016-28-4-509
    Journal articles | 2016
    2016, 'Summation equations with sign changing kernels and applications to discrete fractional boundary value problems', Commentationes Mathematicae Universitatis Carolinae, 57, pp. 201 - 229, http://dx.doi.org/10.14712/1213-7243.2015.164
    Journal articles | 2016
    2016, 'Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions', Advances in Difference Equations, 2016, pp. 1 - 31, http://dx.doi.org/10.1186/s13662-016-0760-3
    Journal articles | 2016
    2016, 'The relationship between sequential fractional differences and convexity', Applicable Analysis and Discrete Mathematics, 10, pp. 345 - 365, http://dx.doi.org/10.2298/AADM161005025G
    Journal articles | 2015
    2015, 'Coupled systems of boundary value problems with nonlocal boundary conditions', Applied Mathematics Letters, 41, pp. 17 - 22, http://dx.doi.org/10.1016/j.aml.2014.10.010
    Journal articles | 2015
    2015, 'Erratum to: A monotonicity result for discrete fractional difference operators[Arch. Math.(2014), 102, 293-299, DOI 10.1007/s00013-014-0620-x]', Archiv der Mathematik, 104, pp. 599 - 600, http://dx.doi.org/10.1007/s00013-015-0771-4
    Journal articles | 2015
    2015, 'On positive solutions to fractional difference inclusions', Analysis (Germany), 35, pp. 73 - 83, http://dx.doi.org/10.1515/anly-2012-1281
    Journal articles | 2015
    2015, 'Partial Hölder continuity of minimizers of functionals satisfying a VMO condition', Advances in Calculus of Variations, 2015, pp. 83 - 110, http://dx.doi.org/10.1515/acv-2015-0013
    Journal articles | 2015
    2015, 'Partial hölder continuity of minimizers of functionals satisfying a general asymptotic relatedness condition', Journal of Convex Analysis, 22, pp. 219 - 246
    Journal articles | 2015
    2015, 'Semipositone boundary value problems with nonlocal, nonlinear boundary conditions', Advances in Differential Equations, 20, pp. 117 - 142
    Journal articles | 2015
    2015, 'Systems of discrete fractional boundary value problems with nonlinearities satisfying no growth conditions', Journal of Difference Equations and Applications, 21, pp. 437 - 453, http://dx.doi.org/10.1080/10236198.2015.1013537
    Journal articles | 2014
    2014, 'A convexity result for fractional differences', Applied Mathematics Letters, 35, pp. 58 - 62, http://dx.doi.org/10.1016/j.aml.2014.04.013
    Journal articles | 2014
    2014, 'A monotonicity result for discrete fractional difference operators', Archiv der Mathematik, 102, pp. 293 - 299, http://dx.doi.org/10.1007/s00013-014-0620-x
    Journal articles | 2014
    2014, 'A note on semipositone boundary value problems with nonlocal, nonlinear boundary conditions', Archiv der Mathematik, 103, pp. 177 - 187, http://dx.doi.org/10.1007/s00013-014-0678-5
    Journal articles | 2014
    2014, 'On Nonlinear Boundary Conditions Involving Decomposable Linear Functionals', Proceedings of the Edinburgh Mathematical Society, 58, pp. 421 - 439, http://dx.doi.org/10.1017/S0013091514000108
    Journal articles | 2014
    2014, 'On a first-order semipositone boundary value problem on a time scale', Applicable Analysis and Discrete Mathematics, 8, pp. 269 - 287, http://dx.doi.org/10.2298/AADM140812013G
    Journal articles | 2014
    2014, 'Systems of semipositone discrete fractional boundary value problems', Journal of Difference Equations and Applications, 20, pp. 473 - 491, http://dx.doi.org/10.1080/10236198.2013.856073
    Journal articles | 2013
    2013, 'Existence of a positive solution to a nonlocal semipositone boundary value problem on a time scale', Commentationes Mathematicae Universitatis Carolinae, 54, pp. 509 - 525
    Journal articles | 2013
    2013, 'On a Nonlocal BVP with Nonlinear Boundary Conditions', Results in Mathematics, 63, pp. 1351 - 1364, http://dx.doi.org/10.1007/s00025-012-0272-8
    Journal articles | 2013
    2013, 'On nonlinear boundary conditions satisfying certain asymptotic behavior', Nonlinear Analysis, Theory, Methods and Applications, 76, pp. 58 - 67, http://dx.doi.org/10.1016/j.na.2012.07.023
    Journal articles | 2013
    2013, 'On semipositone discrete fractional boundary value problems with non-local boundary conditions', Journal of Difference Equations and Applications, 19, pp. 1758 - 1780, http://dx.doi.org/10.1080/10236198.2013.775259
    Journal articles | 2013
    2013, 'Positive solutions to differential inclusions with nonlocal, nonlinear boundary conditions', Applied Mathematics and Computation, 219, pp. 11071 - 11081, http://dx.doi.org/10.1016/j.amc.2013.05.022
    Journal articles | 2012
    2012, 'Nonlocal systems of BVPs with asymptotically superlinear boundary conditions', Commentationes Mathematicae Universitatis Carolinae, 53, pp. 79 - 97
    Journal articles | 2012
    2012, 'Nonlocal systems of bvps with asymptotically sublinear boundary conditions', Applicable Analysis and Discrete Mathematics, 6, pp. 174 - 193, http://dx.doi.org/10.2298/AADM120329010G
    Journal articles | 2012
    2012, 'On a discrete fractional three-point boundary value problem', Journal of Difference Equations and Applications, 18, pp. 397 - 415, http://dx.doi.org/10.1080/10236198.2010.503240
    Journal articles | 2012
    2012, 'On a first-order semipositone discrete fractional boundary value problem', Archiv der Mathematik, 99, pp. 509 - 518, http://dx.doi.org/10.1007/s00013-012-0463-2
    Journal articles | 2012
    2012, 'On a fractional boundary value problem with fractional boundary conditions', Applied Mathematics Letters, 25, pp. 1101 - 1105, http://dx.doi.org/10.1016/j.aml.2011.11.028
    Journal articles | 2012
    2012, 'On discrete fractional boundary value problems with nonlocal, nonlinear boundary conditions', Communications in Applied Analysis, 16, pp. 459 - 470
    Journal articles | 2012
    2012, 'On discrete sequential fractional boundary value problems', Journal of Mathematical Analysis and Applications, 385, pp. 111 - 124, http://dx.doi.org/10.1016/j.jmaa.2011.06.022
    Journal articles | 2012
    2012, 'On nonlocal BVPs with nonlinear boundary conditions with asymptotically sublinear or superlinear growth', Mathematische Nachrichten, 285, pp. 1404 - 1421, http://dx.doi.org/10.1002/mana.201100210
    Journal articles | 2012
    2012, 'Positive solution for a discrete fractional periodic boundary value problem', Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 19, pp. 545 - 557
    Journal articles | 2012
    2012, 'Positive solutions to boundary value problems with nonlinear boundary conditions', Nonlinear Analysis, Theory, Methods and Applications, 75, pp. 417 - 432, http://dx.doi.org/10.1016/j.na.2011.08.044
    Journal articles | 2012
    2012, 'The existence of a positive solution to a second-order deltanabla p-Laplacian BVP on a time scale', Applied Mathematics Letters, 25, pp. 157 - 162, http://dx.doi.org/10.1016/j.aml.2011.08.005
    Journal articles | 2011
    2011, 'Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions', Computers and Mathematics with Applications, 61, pp. 191 - 202, http://dx.doi.org/10.1016/j.camwa.2010.10.041
    Journal articles | 2011
    2011, 'Existence of a positive solution to a first-order p-Laplacian BVP on a time scale', Nonlinear Analysis, Theory, Methods and Applications, 74, pp. 1926 - 1936, http://dx.doi.org/10.1016/j.na.2010.10.062
    Journal articles | 2011
    2011, 'Existence of a positive solution to a system of discrete fractional boundary value problems', Applied Mathematics and Computation, 217, pp. 4740 - 4753, http://dx.doi.org/10.1016/j.amc.2010.11.029
    Journal articles | 2011
    2011, 'Existence of a positive solution to systems of differential equations of fractional order', Computers and Mathematics with Applications, 62, pp. 1251 - 1268, http://dx.doi.org/10.1016/j.camwa.2011.02.039
    Journal articles | 2011
    2011, 'On positive solutions to nonlocal fractional and integer-order difference equations', Applicable Analysis and Discrete Mathematics, 5, pp. 122 - 132, http://dx.doi.org/10.2298/AADM110111001G
    Journal articles | 2011
    2011, 'Some new existence results for fractional difference equations', International Journal of Dynamical Systems and Differential Equations, 3, pp. 145 - 162, http://dx.doi.org/10.1504/IJDSDE.2011.038499
    Journal articles | 2010
    2010, 'Continuity of solutions to discrete fractional initial value problems', Computers and Mathematics with Applications, 59, pp. 3489 - 3499, http://dx.doi.org/10.1016/j.camwa.2010.03.040
    Journal articles | 2010
    2010, 'Existence of a positive solution to a class of fractional differential equations', Applied Mathematics Letters, 23, pp. 1050 - 1055, http://dx.doi.org/10.1016/j.aml.2010.04.035
    Journal articles | 2007
    2007, 'The stabilizing effect of noise on the dynamics of a Boolean network', Physica A: Statistical Mechanics and its Applications, 379, pp. 334 - 356, http://dx.doi.org/10.1016/j.physa.2006.12.043

I am interested in nonlocal differential and difference equations.  I have studied such problems both in the context of nonlocal boundary value problems but also in the context of fractional calculus (both discrete and continuous), which involves inherently nonlocal operators.  I also have an interest in regularity theory for elliptic PDEs and minimizers of variational problems, and I am particularly interested in problems that involve rough or discontinuous coefficients and how such coefficients affect the regularity of any solution or minimizer.