二阶次二次差分方程的同宿轨

Homoclinic solutions for subquadratic second-order difference equations

考虑了二阶次二次差分方程Δ2xn-1-A(n)xn+V(n,xn)=0在无周期条件时的同宿轨问题.仅对A(n)与V加适当的条件,运用临界点理论得到了关于其同宿轨的存在性结果.

In this paper we consider the existence of homoclinic solutions for the following subquadratic second- order difference equations △^2xn-1-A（n）xn＋△↓V（n,xn）=0 .Adopting some reasonable assumptions for A and V,we obtain a new criterion for guaranteeing the above equations which have one nontrivial homoclinie solution by use of a standard minimizing argument in critical point theory.