Infinitely many periodic solutions for differential equations involving piecewise alternately advanced and retarded argument

Abstract

The manuscript introduces an innovative framework for establishing the existence of infinitely many nontrivial periodic solutions within a class of differential equations characterized by a piecewise alternately advanced and retarded argument. It comprehensively delineates the essential criteria required for the existence of these solutions and provides detailed procedures for their determination. Additionally, the study incorporates illustrative examples, including cases with infinitely many solutions, to demonstrate the effectiveness and applicability of the proposed approach.