Firstly,we use Nehari manifold and Mountain Pass Lemma to prove an existence result of positive solutions for a class of nonlocal elliptic system with Kirchhoff type.Then a multiplicity result is established by cohomo...Firstly,we use Nehari manifold and Mountain Pass Lemma to prove an existence result of positive solutions for a class of nonlocal elliptic system with Kirchhoff type.Then a multiplicity result is established by cohomological index of Fadell and Rabinowitz.We also consider the critical case and prove existence of positive least energy solution when the parameter β is sufficiently large.展开更多
A 2-coupled nonlinear Schrbdinger equations with bounded varying potentials and strongly attractive interactions is considered. When the attractive interaction is strong enough, the existence of a ground state for suf...A 2-coupled nonlinear Schrbdinger equations with bounded varying potentials and strongly attractive interactions is considered. When the attractive interaction is strong enough, the existence of a ground state for sufficiently small Planck constant is proved. As the Planck constant approaches zero, it is proved that one of the components concentrates at a minimum point of the ground state energy function which is defined in Section 4.展开更多
基金Supported by National Natural Science Foundation of China(1152618311371313+3 种基金11401121)the Natural Science Foundation of Shanxi Province(2015021015)Foundation of Yuncheng University(YQ-2014011XK-2014035)
基金Supported by the National Natural Science Foundation of China(No.11325107,11271353,11331010)
文摘Firstly,we use Nehari manifold and Mountain Pass Lemma to prove an existence result of positive solutions for a class of nonlocal elliptic system with Kirchhoff type.Then a multiplicity result is established by cohomological index of Fadell and Rabinowitz.We also consider the critical case and prove existence of positive least energy solution when the parameter β is sufficiently large.
基金Research Project of Shanghai Municipal Education Commission(No.07zz83).
文摘A 2-coupled nonlinear Schrbdinger equations with bounded varying potentials and strongly attractive interactions is considered. When the attractive interaction is strong enough, the existence of a ground state for sufficiently small Planck constant is proved. As the Planck constant approaches zero, it is proved that one of the components concentrates at a minimum point of the ground state energy function which is defined in Section 4.
