Existence and infinity of periodic solutions of some second order differential equations with isochronous potentials

In this paper, we deal with the existence and infinity of periodic solutions of differential equations, $$x^{\prime\prime}+f(x^{\prime})+V^{\prime}(x)+g(x)=p(t),$$ where V is a 2??/n-isochronous potential. When f, g are bounded, we give sufficient conditions to ensure the existence of periodic solutions of this equation. We also prove that the given equation has infinitely many 2??-periodic solutions under resonant conditions by using the topological degree approach.