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

摘要

This paper is concerned with the following nonlinear second-order nonautonomous problem: (u) double over dot (t) + q (t) (u) over dot (t) - del K(t,u(t)) + del W(t,u(t)) = 0, where t epsilon R, u epsilon R-N, and K,W epsilon C-1 (R x R-N, R) are not periodic in t and q : R -> R is a continuous function and Q(t) = integral(t)(0)q(s)ds with lim(vertical bar t vertical bar ->+infinity)Q(t) = +infinity. The existence andmultiplicity of fast homoclinic solutions are established by using Mountain Pass Theorem and Symmetric Mountain Pass Theorem in critical point theory.