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POSITIVE SOLUTIONS FOR WEAKLY COUPLED NONLINEAR ELLIPTIC SYSTEMS 被引量：1

POSITIVE SOLUTIONS FOR WEAKLY COUPLED NONLINEAR ELLIPTIC SYSTEMS
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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.
作者 龙静 杨健夫
机构地区 Wuhan Institute of Physics and Mathematics Graduate School Department of Mathematics
出处 《Acta Mathematica Scientia》 SCIE CSCD 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)
关键词 Elliptic system in RN positive solution BIFURCATION variational method Elliptic system in RN positive solution bifurcation variational method
分类号 O175.25 [理学—基础数学] O469 [理学—凝聚态物理]
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Acta Mathematica Scientia
2010年 第5期

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