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