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A study of a nonlinear ordinary differential equation in modular function spaces endowed with a graph. (English) Zbl 1461.34020

Summary: In this paper, we prove by means of a fixed-point theorem an existence result of the Cauchy problem associated to an ordinary differential equation in modular function spaces endowed with a reflexive convex digraph.

MSC:

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
05C20 Directed graphs (digraphs), tournaments
47N20 Applications of operator theory to differential and integral equations
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