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.
The existence of a nontrivial solution to the Schrodinger-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.
作者
冯晓晶
Feng Xiaojing(School of Mathematical Sciences,Shanxi University,Taiyuan 030006)
出处
《数学物理学报（A辑）》
CSCD
北大核心
2020年第6期1590-1598,共9页
Acta Mathematica Scientia
基金
国家自然科学基金(11571209,11671239)
山西省自然科学基金(201801D211001,201801D121002,201801D221012)
山西省留学基金(020-005)。
关键词
薛定谔-泊松系统
临界指数
变分方法
Schrödinger-Poisson type system
Critical exponent
Variational method
