Maximum principles for ordinary and parital dynamic equations

Abstract:

Motivated by the importance of maximum principles in the theory of partial differential equations and in the numerical analysis, we establish simple maximum principles for basic partial dynamic operators on multidimensional time scales. As in the case of ordinary dynamic operators we reveal a set of results and counterexamples which illustrate the distinct behaviour in continuous and discrete case.

Finally, we provide some immediate consequences and prove uniqueness results to problems involving partial dynamic operators.