Boundary Value Problems
Volume 2010 (2010), Article ID 586971, 8 pages
Research Article

Periodic Problem with a Potential Landesman Lazer Condition

Department of Mathematics, University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech Republic

Received 6 January 2010; Revised 30 June 2010; Accepted 22 September 2010

Academic Editor: Pavel Drábek

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.


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.