R^(4)中一类Kirchhoff方程的高能量径向解的存在性

为解决物理领域中用来描述弹性弦在横向振动过程中弦长变化模型的求解问题,基于变分方法,研究了一类具有一般非线性项的a+b型Kirchhoff方程高能量径向解的存在性问题。通过选择合适的变分框架,首先,一方面给出了一般非线性项f满足的一般性条件且给出了满足条件的具体例子,另一方面通过放缩构造了与该Kirchhoff方程有关的两个能量泛函;其次,借助Pohožaev恒等式来构造具有特殊性质的序列以解决Palais-Smale序列的有界性问题;最后,利用对称山路引理建立该类Kirchhoff方程高能量径向解的存在性结果。

具有一般非线性项的拟线性Choquard方程的基态解

研究了一类广义拟线性Choquard方程基态解的存在性问题,利用变量替换与变分方法,证明了该方程基态解的存在性定理.所得结果推广并补充了原有结论.

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 .

Existence of Sign-Changing Solution with Least Energy for a Class of Schrödinger-Poisson Equations in R³

The nodal solutions of equations are considered to be more difficult than the positive solutions and the ground state solutions. Based on this, this paper intends to study nodal solutions for a kind of Schrödinger-Poisson equation. We consider a class of Schrödinger-Poisson equation with variable potential under weaker conditions in this paper. By introducing some new techniques and using truncated functional, Hardy inequality and Pohožaev identity, we obtain an existence result of a least energy sign-changing solution and a ground state solution for this kind of Schrödinger-Poisson equation. Moreover, the energy of the sign-changing solution is strictly greater than the ground state energy.