POSITIVE SOLUTIONS FOR WEAKLY COUPLED NONLINEAR ELLIPTIC SYSTEMS  

作　　者：龙静 杨健夫 

机构地区：[1]Wuhan Institute of Physics and Mathematics,Chinese Academy of Sciences [2]Graduate School,Chinese Academy of Sciences [3]Department of Mathematics,Jiangxi Normal University

出　　处：《Acta Mathematica Scientia》2010年第5期1577-1592,共16页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundations of China(10631030,10961016)

摘　　要：In this article, we consider the existence of positive solutions for weakly coupled nonlinear elliptic systems {-△u＋u=（1＋a（x））｜u｜P-1u＋μ｜u｜a-2u｜v｜β＋λv in Rn,-△u＋u=（1＋b（x））｜v｜p-1v＋μ｜u｜a｜v｜β-2v＋λu in Rn To find nontrivial solutions, we first investigate autonomous systems. In this case, results of bifurcation from semi-trivial solutions are obtained by the implicit function theorem. Next, the existence of positive solutions of problem （0.1） is obtained by variational methods.In this article, we consider the existence of positive solutions for weakly coupled nonlinear elliptic systems {-△u＋u=（1＋a（x））｜u｜P-1u＋μ｜u｜a-2u｜v｜β＋λv in Rn,-△u＋u=（1＋b（x））｜v｜p-1v＋μ｜u｜a｜v｜β-2v＋λu in Rn To find nontrivial solutions, we first investigate autonomous systems. In this case, results of bifurcation from semi-trivial solutions are obtained by the implicit function theorem. Next, the existence of positive solutions of problem （0.1） is obtained by variational methods.

关 键 词：Elliptic system in RN positive solution BIFURCATION variational method 

分 类 号：O175.25[理学—数学] O469[理学—基础数学]