摘要
研究了下述非线性Schrdinger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.
出处
《华中师范大学学报(自然科学版)》
CAS
北大核心
2015年第5期657-664,共8页
Journal of Central China Normal University:Natural Sciences
基金
The Fund from NSF of China(11125101)
Program for Changjiang Scholars and Innovative Research Team in University(IRT13066)