Article ID Journal Published Year Pages File Type
4618537 Journal of Mathematical Analysis and Applications 2011 13 Pages PDF
Abstract

This paper is concerned with the existence of homoclinic solutions for the following second order non-autonomous systemequation(FHS)q¨+cq˙+Uq(t,q)=0, where q∈Rnq∈Rn, c⩾0c⩾0 is a constant and U(t,q)∈C1(R×Rn,R)U(t,q)∈C1(R×Rn,R). Under some reasonable assumptions, for the first time we introduce the concept of fast homoclinic solutions of (FHS) and establish some criteria to guarantee the existence of fast homoclinic solutions of (FHS). Besides that, in some particular case, the uniqueness of homoclinic solutions of (FHS) is also obtained. Recent results in the literature are generalized and significantly improved.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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