Invariant Curves of Almost Periodic Reversible Mappings

Abstract

In this paper, we prove some invariant curve theorems for the planar almost periodic reversible mappings. As an application, we will discuss the existence of almost periodic solutions and the boundedness of all solutions for the nonlinear oscillator $x"+g(x)x^{\prime }+{\varpi }^{2}x+\phi (x)=f(t)$ with $f(t)$ almost periodic.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1606.08938, arXiv:1705.09162 by other authors