Periodic solutions for a class of conservative Liénard-type equations

Abstract

In this paper, we study solvability of a class of second-order differential equations in a conservative Liénard form subject to periodic boundary conditions. Results on existence of non-trivial T-periodic solutions or positive T-periodic solutions are obtained respectively. Applications of the theorems are shown by examples. The results are proved by applying the coincidence degree theory for semilinear operator equations.