科研之友
微信
新浪微博
Facebook
分享链接
摘要
This paper deals with the following nonlinear elliptic problem @@@ (0, 1) -epsilon(2)Delta u + omega V(x)u = u(p) + u(2)*(-1), u > 0 in R-N, @@@ where omega is an element of R+, N >= 3, p is an element of (1, 2* - 1) with 2* = 2N/(N - 2), is an element of > 0 is a small parameter and V(x) is a given function. Under suitable assumptions, we prove that problem (0.1) has multi-peak solutions by the Lyapunov-Schmidt reduction method for sufficiently small epsilon, which concentrate at local minimum points of potential function V(x). Moreover, we show the local uniqueness of positive multi-peak solutions by using the local Pohozaev identity.
