数学物理学报 ›› 2020, Vol. 40 ›› Issue (6): 1590-1598.

• 论文 • 上一篇    下一篇

带有双临界项的薛定谔-泊松系统非平凡解的存在性

冯晓晶()   

  1. 山西大学数学科学学院 太原 030006
  • 收稿日期:2019-11-06 出版日期:2020-12-26 发布日期:2020-12-29
  • 作者简介:冯晓晶, E-mail: fengxj@sxu.edu.cn
  • 基金资助:
    国家自然科学基金(11571209);国家自然科学基金(11671239);山西省自然科学基金(201801D211001);山西省自然科学基金(201801D121002);山西省自然科学基金(201801D221012);山西省留学基金(020-005)

Nontrivial Solution for Schrödinger-Poisson type Systems with Double Critical Terms

Xiaojing Feng()   

  1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006
  • Received:2019-11-06 Online:2020-12-26 Published:2020-12-29
  • Supported by:
    the NSFC(11571209);the NSFC(11671239);NSF of Shanxi Province(201801D211001);NSF of Shanxi Province(201801D121002);NSF of Shanxi Province(201801D221012);the Shanxi Scholarship Council(020-005)

摘要:

该文利用集中紧性原理和山路定理, 研究了一类具有非线性临界增长和非局部临界增长的薛定谔-泊松系统非平凡解的存在性.系统中的双临界增长项对有界(PS)序列的收敛性造成一定的困难.此外, 山路的水平也较难估计.该文关键之处在于证明山路的临界水平值低于相应能量泛函的非紧性水平.

关键词: 薛定谔-泊松系统, 临界指数, 变分方法

Abstract:

The existence of a nontrivial solution to the Schrödinger-Poisson type system with both nonlinear critical growth and nonlocal critical growth is obtained by applying the concentration-compactness principle and mountain pass theorem. The double critical growth in the system presents an obstacle when showing the convergence of the bounded (PS) sequences. At the same time, it is difficult to estimate the critical level of the mountain pass. The key ingredient of the paper is to show that the critical level of the mountain pass is below the non-compactness level of the associated energy functional.

Key words: Schrödinger-Poisson type system, Critical exponent, Variational method

中图分类号: 

  • O175.2