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Nonlocal initial value problems for first-order dynamic equations on time scales. (English) Zbl 1498.34241

Summary: This article is concerned with a class of first-order dynamic equations on time scales with nonlocal initial conditions. Qualitative and quantitative results are discussed. Through an application of a fixed point theorem due to O’Regan, the existence of solutions is investigated. Under suitable assumptions, we deduce the existence result for nonlocal dynamic Cauchy problem. We also examine the continuous dependency of solutions on initial conditions. We illustrate our main result through examples.

MSC:

34N05 Dynamic equations on time scales or measure chains
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
39A12 Discrete version of topics in analysis
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