Periodic Problem with a Potential Landesman Lazer Condition. (26th September 2010)

• Record Type: Journal Article
• Authors: Tomiczek Tomiczek, Petr Petr
• Other Names: Drábek Drábek Pavel Pavel Academic Editor.
• Is Part Of: Boundary value problems. Volume 2010(2010)
• Publication Date: 2010-09-26
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2010/586971
• Languages: English
• ISSNs: 1687-2762

Abstract

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 ∫ 0 T r ( x ) d x = 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.