Existence of fast homoclinic orbits for a class of second-order non-autonomous problems
1 College of Science, Guilin University of Technology, Guilin, Guangxi, 541004, P.R. China
2 College of Science, Hunan University of Technology, Zhuzhou, Hunan, 412000, P.R. China
3 School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan, 410083, P.R. China
Boundary Value Problems 2014, 2014:89 doi:10.1186/1687-2770-2014-89Published: 6 May 2014
By applying the mountain pass theorem and the symmetric mountain pass theorem in critical point theory, the existence and multiplicity of fast homoclinic solutions are obtained for the following second-order non-autonomous problem: , where , , , , are not periodic in t and is a continuous function and with .
MSC: 34C37, 35A15, 37J45, 47J30.