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

Abstract

In this paper, we study the $T$-periodic solutions of the parameter-dependent $\varphi$-Laplacian equation \begin{equation*} (ϕ(x'))'=F(λ,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 Liénard-type equations.

26 pages, 1 figure