A Concentration Behavior for Semilinear Elliptic Systems with Indefinite Weight

论文作者:Xue Xiu ZHONG;Wen Ming ZOU;
作者单位:Department of Mathematical Sciences,Tsinghua University
期刊名称:《Acta Mathematica Sinica(English Series)》
依托项目:Supported by National Natural Science Foundation of China(Grant Nos.11025106; 11271386);
论文摘要: Consider the Schrdinger system{-Δu+V1,nu=αQn(x)︱u︱α-2u︱v︱β,-Δv+V2,nv=βQn(x)︱u︱α︱v︱β-2v,u,v∈H10(Ω) where ΩRN,α,β> 1,α + β< 2* and the spectrum σ(-△ + Vi,n)(0,+∞),i = 1,2;Qn is a bounded function and is positive in a region contained in Ω and negative outside.Moreover,the sets{Qn > 0} shrink to a point x0∈Ω as n→+∞.We obtain the concentration phenomenon.Precisely,we first show that the system has a nontrivial solution(un...