Existence and Multiplicity of Fast Homoclinic Solutions for a Class of Nonlinear Second-Order Nonautonomous Systems in a Weighted Sobolev Space. (22nd June 2015)

• Record Type: Journal Article
• Authors: Zhang, Qiongfen; Li, Yuan
• Other Names: Sawano Yoshihiro Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-06-22
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/495040
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : This paper is concerned with the following nonlinear second-order nonautonomous problem:u ̈ ( t ) + q ( t ) u ̇ ( t ) - ∇ K ( t, u ( t ) ) + ∇ W ( t, u ( t ) ) = 0, wheret ∈ R, u ∈ R N, andK, W ∈ C 1 ( R × R N, R ) are not periodic int andq : R → R is a continuous function andQ ( t ) = ∫ 0 t ‍ q ( s ) d s withlim | t | → + ∞ ⁡ Q ( t ) = + ∞ . The existence and multiplicity of fast homoclinic solutions are established by using Mountain Pass Theorem and Symmetric Mountain Pass Theorem in critical point theory.