On the existence of periodic solutions for Liénard type $φ$-Laplacian equation - Yang, Congmin; Wang, Zaihong (Topological Methods in Nonlinear Analysis, 2023)
In this paper, we study the existence of periodic solutions for a Liénard type$φ$-Laplacian equation$$(φ(x'))'+f(x)x'+g(x)=p(t).$$We prove a continuation lemma and use it to prove the existence of periodicsolutions for above equation when $g$ or $G$ (the primitive of $g$) satisfies some one-sided or bilateral growth conditionsand $F$ (the primitive of $f$) satisfies sublinear condition.