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Exact and approximate solutions of delay differential equations with nonlocal history conditions. (English) Zbl 1098.34573

Summary: We study the exact and approximate solutions of a delay differential equation with various types of nonlocal history conditions. We establish the existence and uniqueness of mild, strong, and classical solutions for a class of such problems using the method of semidiscretization in time. We also establish a result concerning the global existence of solutions. Finally, we consider some examples and discuss their exact and approximate solutions.

MSC:

34K30 Functional-differential equations in abstract spaces
35R10 Partial functional-differential equations
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