No abstract

In this paper, we consider the following Neumann problemwhere n ≥ 3, ε is a small positive parameter, and K is a positive and bounded function in R n−1 . By variational method, we prove the existence of peak solution that concentrate around one critical point of K satisfying certain conditions.

The main purpose of this paper is to construct sign‐changing solution for the following Neumann problem: (P):Δu=0,inR+n,and−∂u∂xn=K(x)|u|2n−2uon∂R+n, where n≥3 and K is a bounded and continuous function on double-struckRn−1, which concentrate around two critical points satisfying some conditions. Copyright © 2016 John Wiley & Sons, Ltd.