Periodic solutions and asymptotic behavior in Liénard systems with p-Laplacian operators

Abstract

We first prove the existence of periodic solutions to systems of the form \[ (\phi_{p}(u^{\prime}))^{\prime}+\frac{d}{dt}(\nabla F(u))+\nabla G(u)=e(t). \] We then study the asymptotic behavior of all solutions to such systems, and give sufficient conditions for uniform ultimate boundedness of solutions.