Periodic Problem with a Potential Landesman Lazer Condition. (26th September 2010) - Tomiczek, Petr
Abstract : We prove the existence of a solution to the periodic nonlinear second-order ordinary differential equation with dampingu ″ ( x ) + r ( x ) u ' ( x ) + g ( x, u ( x ) ) = f ( x ), u ( 0 ) = u ( T ), u ' ( 0 ) = u ' ( T ) . We suppose that∫ 0 T r ( x ) d x = 0, the nonlinearityg satisfies the potential Landesman Lazer condition and prove that a critical point of a corresponding energy functional is a solution to this problem.