带Choquard项的拟线性薛定谔方程的基态解

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 730-748.

带Choquard项的拟线性薛定谔方程的基态解

王亚男(),滕凯民*()

^{太原理工大学数学学院山西晋中 030600}

收稿日期:2021-04-14 出版日期:2022-06-26 发布日期:2022-05-09
通讯作者: 滕凯民 E-mail:862240639@qq.com;tengkaimin2013@163.com
作者简介:王亚男, E-mail: 862240639@qq.com
基金资助:
国家自然科学基金(11501403);山西省留学回国择优项目(2018);山西省自然科学基金面上项目(201901D111085)

Ground State Solutions for Quasilinear Schrödinger Equation of Choquard Type

Yanan Wang(),Kaimin Teng*()

^{School of Mathematical, Taiyuan University of Technology, Shanxi Jinzhong 030600}

Received:2021-04-14 Online:2022-06-26 Published:2022-05-09
Contact: Kaimin Teng E-mail:862240639@qq.com;tengkaimin2013@163.com
Supported by:
the NSFC(11501403);the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province(2018);the NSF of Shanxi Province(201901D111085)

摘要/Abstract

摘要：

该文研究如下Choquard型拟线性薛定谔方程 $ \begin{eqnarray*} -\triangle u+\frac{k}{2}u\triangle u^2+V(x)u=(I_{\alpha}\ast|u|^{p})|u|^{p-2}u, \, \, x\in\mathbb{R}^N, \end{eqnarray*} $ 其中$N\geq3$, 0 < $\alpha$ < $N$, $< p<\frac{N+\alpha}{N-2}$, $I_{\alpha}$是Riesz位势, $V(x)$是一个正连续位势, $k$是一个非负参数. 采用Pohožaev流形方法, 证明了基态解的存在性.

关键词: Choquard型方程, Pohožaev流形, 基态解

Abstract:

In this paper, we consider the following quasilinear Schrödinger equations of Choquard type $ \begin{eqnarray*} -\triangle u+\frac{k}{2}u\triangle u^2+V(x)u=(I_{\alpha}\ast|u|^{p})|u|^{p-2}u, \, \, x\in\mathbb{R}^N, \end{eqnarray*} $ where $N\geq3$, 0 < $\alpha$ < $N$, $<p<\frac{N+\alpha}{N-2}$, $I_{\alpha}$ is the Riesz potential, $V(x)$ is a positive continuous potential and $k$ is a non-negative parameter. The existence of ground state solutions is established via Pohožaev manifold approach.

Key words: Choquard type problems, Pohožaev manifold, Ground state solutions

中图分类号:

O175.25

王亚男,滕凯民. 带Choquard项的拟线性薛定谔方程的基态解[J]. 数学物理学报, 2022, 42(3): 730-748.

Yanan Wang,Kaimin Teng. Ground State Solutions for Quasilinear Schrödinger Equation of Choquard Type[J]. Acta mathematica scientia,Series A, 2022, 42(3): 730-748.

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