In this article, we establish a nonexistence result of nontrivial non-negative solutions for the following Choquard-type Hamiltonian system by the Pohožaev identity , when , , , , , and , where and denotes the convolu...In this article, we establish a nonexistence result of nontrivial non-negative solutions for the following Choquard-type Hamiltonian system by the Pohožaev identity , when , , , , , and , where and denotes the convolution in .展开更多
In this paper,we show the scattering of the radial solution for the nonlinear Schrodinger equation with combined power-type and Choquard-type nonlinearities iut+△u=λ1|u|p1-1u+λ2(Iα*|u|^(p2))|u|p^(2-2)u.in the ener...In this paper,we show the scattering of the radial solution for the nonlinear Schrodinger equation with combined power-type and Choquard-type nonlinearities iut+△u=λ1|u|p1-1u+λ2(Iα*|u|^(p2))|u|p^(2-2)u.in the energy space H^(1)(R^(N))forλ_(1)λ_(2)=-1.We establish a scattering criterion for radial solution together with Morawetz estimate which implies the scattering theory.Results show that the defocusing perturbation terms does not determine the scattering solution in energy space.展开更多
In this article, we study the nonexistence of solution with finite Morse index for the following Choquaxd type equation -△u=∫Rn｜u（y）｜p/｜x-y｜αdy｜u（x）｜p-2u（x） in RN,where N≥3,0〈α〈min {4,N}.Suppose tha...In this article, we study the nonexistence of solution with finite Morse index for the following Choquaxd type equation -△u=∫Rn｜u（y）｜p/｜x-y｜αdy｜u（x）｜p-2u（x） in RN,where N≥3,0〈α〈min {4,N}.Suppose that 2 〈 p 〈2N-α/N-2,we will show that this problem does not possess nontrivial solution with finite Morse index. While for p =2N-α/N-2,if i（u） 〈∞, then we have ∫RN∫RN｜u（x）｜p｜u（y）｜p dxdy 〈∞ and ∫RN｜△u｜2 dx=｜∫RN∫RN｜u（x）｜p/｜x-y｜a dxdy.展开更多
文摘In this article, we establish a nonexistence result of nontrivial non-negative solutions for the following Choquard-type Hamiltonian system by the Pohožaev identity , when , , , , , and , where and denotes the convolution in .
文摘In this paper,we show the scattering of the radial solution for the nonlinear Schrodinger equation with combined power-type and Choquard-type nonlinearities iut+△u=λ1|u|p1-1u+λ2(Iα*|u|^(p2))|u|p^(2-2)u.in the energy space H^(1)(R^(N))forλ_(1)λ_(2)=-1.We establish a scattering criterion for radial solution together with Morawetz estimate which implies the scattering theory.Results show that the defocusing perturbation terms does not determine the scattering solution in energy space.
文摘In this article, we study the nonexistence of solution with finite Morse index for the following Choquaxd type equation -△u=∫Rn｜u（y）｜p/｜x-y｜αdy｜u（x）｜p-2u（x） in RN,where N≥3,0〈α〈min {4,N}.Suppose that 2 〈 p 〈2N-α/N-2,we will show that this problem does not possess nontrivial solution with finite Morse index. While for p =2N-α/N-2,if i（u） 〈∞, then we have ∫RN∫RN｜u（x）｜p｜u（y）｜p dxdy 〈∞ and ∫RN｜△u｜2 dx=｜∫RN∫RN｜u（x）｜p/｜x-y｜a dxdy.
