Positive Periodic Solutions to Lie´nard Equation with Indefinite Weights
Ruina Zhao *
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, China.
Shujing Yuan
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, China.
*Author to whom correspondence should be addressed.
Abstract
The Liénard equation is not only of significant theoretical interest but also plays a fundamental role in physical modeling. In particular, Liénard equations with indefinite weights introduce additional complexities that render their analysis more challenging. This paper establishes sufficient conditions for the existence of positive periodic solutions to a class of generalized Liénard equations with sign-changing coefficients. Our approach is primarily based on the Krasnoselskii’s-Guo fixed point theorem, combined with the positivity properties of the associated Green function.
Keywords: Periodic solution, Liénard equation, indefinite singularity, Krasnoselskii’s-Guo fixed point theorem