数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 475-483.

• 论文 • 上一篇    下一篇

临界情形下Schrödinger-Maxwell方程的基态解

方立婉1(),黄文念2(),汪敏庆2()   

  1. 1 广西科技师范学院数学与计算机科学学院 广西来宾 546199
    2 广西师范大学数学与统计学院 广西桂林 541004
  • 收稿日期:2017-04-28 出版日期:2019-06-26 发布日期:2019-06-27
  • 作者简介:方立婉, fangliwan1992@163.com|黄文念, csuhuangwn@163.com|汪敏庆, hgncwangmq@126.com
  • 基金资助:
    广西师范大学科学研究基金(2014ZD001);广西自然科学基金(2015GXNSFBA139018);2017广西研究生教育创新计划项目(XYCZ2017074)

Ground-State Solutions for Schrödinger-Maxwell Equations in the Critical Growth

Liwan Fang1(),Wennian Huang2(),Minqing Wang2()   

  1. 1 School of Mathematics and Computer Science, Guangxi Science and Technology Normal University; Guangxi Laibin 546199
    2 School of Mathematics and Statistics, Guangxi Normal University, Guangxi Guilin 541004
  • Received:2017-04-28 Online:2019-06-26 Published:2019-06-27
  • Supported by:
    the Science Research Fund of Guangxi Normal University(2014ZD001);the Natural Science Foundation of Guangxi(2015GXNSFBA139018);the Postgraduate Education Innovation Plan Project of Guangxi in 2017(XYCZ2017074)

摘要:

该文主要研究下面的Schrödinger-Maxwell方程

基态解的存在性,其中β是正常数.当VK以及bx)满足某些假设条件时,运用变分法和临界点理论,可以证明当α < 0和p∈(3,4)时,上面的方程至少存在一个基态解.

关键词: Schrödinger-Maxwell方程, 临界点理论, 临界情形, 基态解, Nehari流形

Abstract:

In this paper, we study the existence of the ground state solutions for the following Schrödinger-Maxwell equations

where β is a positive constant. Under some assumptions on V, K and b(x), by using the variational method and critical point theorem, we prove that such a class of equations has at least a ground state solution for α < 0 and p ∈ (3, 4).

Key words: Schrödinger-Maxwell equations, Critical point theorem, Critical growth, Ground state solution, Nehari manifold

中图分类号: 

  • O175.25