中文摘要：

研究了下述非线性Schrodinger方程{-Δu＋（1＋βV（y））u=｜u｜p-2u,y∈RN,{U（y）→0,当｜y｜→＋∞非径向对称的变号解的存在性.其中2〈pM2N/（N-2）^＋,β是一个参数，V（y）〉0为满足指数衰减的权函数.当β→-∞（或0-）时,对任意正整数k〉1,构造了上述方程恰好有k个极大值点和k个极小值点的非径向对称的变号解.

英文摘要：

This paper is concerned with the existence of multiple non-radial sign-changing solutions for{-Δu＋（1＋βV（y））u=｜u｜p-2u,y∈RN,{U（y）→0,当｜y｜→＋∞ where 2〈pM2N/（N-2）^＋,for N 〉 2 and 2 ＊ =＋∞ for N = 2, β can be regarded as a parameter and V（ ｜ y ｜ ） 〉 0 decays exponentially to zero at infinity. We prove that there exists a suitable range of β such that the above problem has a non-radial sign-changing solutions with exactly k maximum points and k min- imum points which tend to infinity as fl --β→- ∞ （ or 0^- ） for any positive integer k〉 1.