Copyright © 2010 Petr Tomiczek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove the existence of a solution to the periodic nonlinear second-order ordinary differential equation with damping u″(x)+r(x)u'(x)+g(x,u(x))=f(x), u(0)=u(T), u'(0)=u'(T). We suppose that ∫0Tr(x)dx=0, the nonlinearity g satisfies the potential Landesman Lazer condition and prove that a critical point of a corresponding energy functional is a solution to this problem.