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

In this paper, we study the $T$-periodic solutions of the parameter-dependent $\phi$-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.