Atypical bifurcation for periodic solutions of $\phi$-Laplacian systems

TL;DR

This paper investigates the bifurcation of periodic solutions in $\

Contribution

It introduces new atypical bifurcation results for $\

Findings

Bifurcation of $T$-periodic solutions from $\

Application to Liénard-type equations,

Use of topological degree theory

Abstract

In this paper, we study the $T$-periodic solutions of the parameter-dependent $\phi$-Laplacian equation \begin{equation*} (\phi(x'))'=F(\lambda,t,x,x'). \end{equation*} Based on the topological degree theory, we present some atypical bifurcation results in the sense of Prodi-Ambrosetti, i.e., bifurcation of $T$-periodic solutions from $\lambda=0$. Finally, we propose some applications to Li\'enard-type equations.