Multi-peak Nodal Solutions for a Two-dimensional Elliptic Problem with Large Exponent in Weighted Nonlinearity

作     者：Yi-bin ZHANG Hai-tao YANG 

作者机构：College of Sciences Nanjing Agricultural University Department of Mathematics Zhejiang University 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2015年第31卷第1期

页      面：261-276页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(No.11171214) 

主　　题：multi-peak nodal solutions large exponent finite dimensional reduction 

摘      要：We consider the boundary value problem△u＋︳x︳^2α︳u︳p-1u=0,-1〈α≠*** the unit ballB with the homogeneous Dirichlet boundary condition, when p is a large exponent. By a constructive way, weprove that for any positive integer m, there exists a multi-peak nodal solution vp whose maxima and minima arelocated alternately near the origin and the other m points q1=（λcos^2Л（1-1）/m,λsin 2Л（1-1）/m,1=2,…,m＋1such that as p goes to ＋∞ ,p︳x︳2α︳up︳p-1 up→8Лe（1＋α）（1＋α）δ0＋∑^m＋1δ_1=28Лe（-1）l-1δql,whereλ∈（0, 1）, m is an odd number with（1＋α）（m＋2） -- 1 〉 0, or m is an even number. The same techniqueslead also to a more general result on general domains.