On Periodic Solutions for $p(x)$-Laplacian Problems With Leray-Schauder Degree Theory

Abstract

In this paper, we delve into the existence of nonnegative periodic solutions for a distinct class of $p(x)$-Laplacian problems with nonlocal terms. Employing the parabolic regularization method coupled with Leray-Schauder degree theory, we establish significant results that advance the understanding of these complex mathematical structures. Our results not only demonstrate the robustness of these methods but also open new pathways for further research in the field of nonlinear analysis and differential equations.