Consider the following system of double coupled Schrodinger equations arising from Bose-Einstein condensates etc., where μ1, μ2 are positive and fixed; κ and β are linear and nonlinear coupling parameters respect...Consider the following system of double coupled Schrodinger equations arising from Bose-Einstein condensates etc., where μ1, μ2 are positive and fixed; κ and β are linear and nonlinear coupling parameters respectively. We first use critical point theory and Liouville type theorem to prove some existence and nonexistence results on the positive solutions of this system. Then using the positive and non-degenerate solution to the scalar equation -△ω ＋ ω = ω3, ω ∈ Hr1（RN）, we construct a synchronized solution branch to prove that for/3 in certain range and fixed, there exist a series of bifurcations in product space R×Hr1（RN）×Hr1（RN） with parameter κ,展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11325107,11271353 and 11331010)the China Postdoctoral Science Foundation
文摘Consider the following system of double coupled Schrodinger equations arising from Bose-Einstein condensates etc., where μ1, μ2 are positive and fixed; κ and β are linear and nonlinear coupling parameters respectively. We first use critical point theory and Liouville type theorem to prove some existence and nonexistence results on the positive solutions of this system. Then using the positive and non-degenerate solution to the scalar equation -△ω ＋ ω = ω3, ω ∈ Hr1（RN）, we construct a synchronized solution branch to prove that for/3 in certain range and fixed, there exist a series of bifurcations in product space R×Hr1（RN）×Hr1（RN） with parameter κ,
