一类非线性Schrdinger方程的变号解（英文）

Sign-changingsolutions for a class of nonlinear Schrdinger equations

研究了下述非线性Schrdinger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<p<2N/(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.

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.