A Nonexistence Result for Choquard-Type Hamiltonian System

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 .

Scattering for the Radial Schrodinger Equation with Combined Power-type and Choquard-type Nonlinearities

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.

具有临界增长的分数阶Choquard-Kirchhoff型问题解的存在性

本文研究一类无界区域上分数阶Choquard-Kirchhoff型问题,此类问题源于横振动中对弦长的非局部测量引起的张力,也可用于刻画量子机械波函数的自引力坍缩.该方程的非线性项包含临界项μ(I_(a)^(*)|u|^(2_(a,s)^(*)-2)u|)和扰动项λf(x)uq-1,其中μ,λ均为正参数,2^(*)_(a,s)为分数阶Hardy-Littlewood-Sobolev临界指数,f(x)为连续函数.本文首先利用Nehari流形及Ekeland变分原理证得问题对应的能量泛函具有Palais-Smale序列,然后对参数μ的上界进行估计,在参数λ和次数q选取适当范围时借助Vitali定理及山路引理获得了问题正解的存在性及多重性.最后,当参数λ充分大时,本文利用强极大值原理及临界点定理建立了问题具有正解及无穷多对不同解的存在性定理.

带消失位势Choquard方程解的存在性

研究了一类非局部Schr9dinger方程解的存在性.运用山路引理和Ekland变分法,利用泛函几何结构和极小化序列得到了方程解的存在性.首次将半线性椭圆方程的相关结果推广到Choquard型消失位势Schr9dinger方程.

一类Choquard型拟线性Schrodinger方程解的存在性

考虑一类Choquard型拟线性Schrodinger方程解的存在性。通过变量替换方法将该方程转化为半线性方程,利用山路定理和变分法证明了该方程在适当条件下非平凡解的存在性。

LIOUVILLE THEOREM FOR CHOQUARD EQUATION WITH FINITE MORSE INDICES

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.

一类Choquard型方程解的存在性

该文研究如下形式的Choquard型方程-△_pu+V(x)|u|^(p-2)u=(|x|^(-(N-α))*F(u))f(u),其中,-△_pu=div(|▽u|^(p-2)▽u)),x=(y,z)∈R^K×R^(N-K).假定混合位势V(y,z)关于y具有周期性,关于z具有强制性,并且非线性项f满足一定的条件,利用变分理论,该文证明了上述Choquard型方程具有山路水平解.

带Choquard项的拟线性薛定谔方程的基态解

该文研究如下Choquard型拟线性薛定谔方程-Δu+k/2u△u^(2)+V(x)u=(I_(α)g*|U)|^(p)|u|^(p-2)u,x∈R^(N),其中N≥3,0<α<N,2<p<N+α/N-2,I_(α)是Riesz位势,V(x)是一个正连续位势,k是一个非负参数,采用Pohozaev流形方法,证明了基态解的存在性。