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｜...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.展开更多
基金supported by National Natural Science Foundations of China(10631030,10961016)
文摘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.
