期限(时间)
符号(数学)
数学
数学物理
数学分析
物理
量子力学
作者
Qi Li,Rui Wang,Xinsheng Du
出处
期刊:Mathematical foundations of computing
[American Institute of Mathematical Sciences]
日期:2024-01-01
摘要
In this paper, we are concerned with a class nonlocal Kirchhoff equation with the term of Choquard$ \begin{align*} -(a+b\int_{\mathbb{R}^N}|\nabla u|^2dx)\triangle u +V(x) u = (I_\alpha*k|u|^p)k(x)|u|^{p-2}u,\; x\in \mathbb{R}^N, \end{align*} $where $ a $ and $ b $ are positive constants. With the help of the Hardy-Littlewood-Sobolev inequality, we showed the existence of the bounded convergent $ (PS)_c $ sequence. Combining with the Mountain pass theorem, we proved the existence of a nontrivial solution for the class nonlocal Kirchhoff equation with the term of Choquard. Furthermore, we also obtained at least one least energy sign-changing solution via the Hardy-Littlewood-Sobolev inequality and Brouwer topological degree.
科研通智能强力驱动
Strongly Powered by AbleSci AI