Existence and nonexistence of limit cycles for Liénard-type equations with bounded nonlinearities and φ-Laplacian

Abstract

This paper deals with an equivalent system to the nonlinear differential equation of Liénard type [Formula: see text], where the range of the function [Formula: see text] is bounded. Sufficient conditions are obtained for the system to have at least one limit cycle. The proofs of our results are based on phase plane analysis of the system with the Poincaré–Bendixon theorem. Moreover, to show that these sufficient conditions are suitable in some sense, we also establish the results that the system has no limit cycles. Finally, some examples are given to illustrate our results.