Periodic solutions for some phi-Laplacian and reflection equations

TL;DR

This paper investigates the existence and periodicity of solutions for certain phi-Laplacian and reflection differential equations, providing explicit period calculations and linking solutions of initial problems to boundary value problems with reflection.

Contribution

It introduces methods to explicitly compute periods of solutions and connects initial differential problems with boundary value problems involving reflection.

Findings

Established existence of periodic solutions for specific phi-Laplacian equations.

Derived explicit formulas for the period of solutions.

Linked solutions of initial problems to boundary value problems with reflection.

Abstract

This work is devoted to the study of the existence and periodicity of solutions of initial differential problems, paying special attention to the explicit computation of the period. These problems are also connected with some particular initial and boundary value problems with reflection, which allows us to prove existence of solutions of the latter using the existence of the first.