本文讨论一类非线性Schrdinger方程-ε~2△v+V(z)v=K(x)v~p,x∈R~N,v∈W~(1,2)(R~N),v(x)>0,势函数V(x)有正下界和在无穷远处为零两种情形.通过强最大值原理我们证明方程的基态解关于充分小的ε>0一致集中.

This paper deals with a class of nonlinear Schrdinger equations-ε~2△v+ V(x)v=K(x)v~p,x∈R~N,v∈W~(1,2)(R~N),v(x)>0,with potential V(x)having a positive lower bound or vanishing at infinity,respectively.By the strong maximum principle we show that the ground states concentrate uniformly in smallε>0.