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Journal of Function Spaces
Volume 2015, Article ID 495040, 11 pages
Research Article

Existence and Multiplicity of Fast Homoclinic Solutions for a Class of Nonlinear Second-Order Nonautonomous Systems in a Weighted Sobolev Space

College of Science, Guilin University of Technology, Guilin, Guangxi 541004, China

Received 20 January 2015; Accepted 8 April 2015

Academic Editor: Yoshihiro Sawano

Copyright © 2015 Qiongfen Zhang and Yuan Li. 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.


This paper is concerned with the following nonlinear second-order nonautonomous problem: , where , , and , are not periodic in and is a continuous function and with . The existence and multiplicity of fast homoclinic solutions are established by using Mountain Pass Theorem and Symmetric Mountain Pass Theorem in critical point theory.