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Some notes on the existence of solution for ordinary differential equations via fixed point theory. (English) Zbl 1469.54108

Summary: We establish a fixed point theorem with \(w\)-distance for nonlinear contractive mappings in complete metric spaces. As applications of our results, we derive the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions. Here, we need not assume that the equation has a lower solution.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
34A34 Nonlinear ordinary differential equations and systems
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