一类带有Hardy项的Schr?dinger-Poisson系统非平凡解的存在性  

Existence of Nontrivial Solution to a Class of Schr?dinger-Poisson System with Hardy Term

作　　者：李宇华[1] 谷花 LI Yuhua;GU Hua(School of Mathematical Sciences,Shanxi University,Taiyuan,030006 tChina)

机构地区：[1]山西大学数学科学学院

出　　处：《山西大学学报（自然科学版）》2019年第4期818-823,共6页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11571209;11671239)

摘　　要：研究了R^3中有界光滑区域上的一类带有Hardy项和对数非线性项的Schrodinger-Poisson系统非平凡解的存在性。在f满足一定条件下,结合Hardy不等式以及对数Sobolev不等式得到能量泛函的山路几何结构,通过山路定理证明了非平凡解的存在性。The existence of nontrivial solution to a class of Schrodinger-Poisson system with Hardy term and logarithmic nonlinearity on a bounded smooth domain in R^3 is studied. Under certain conditions on f, combined with Hardy inequality and logarithmic Sobolev inequality, the mountain pass geometric structure of energy functional can be constructed. Moreover,Mountain Pass Theorem implies the existence of the nontrivial solution.

关 键 词：Schrodinger-Poisson系统 HARDY不等式 对数SOBOLEV不等式 

分 类 号：O175.25[理学—数学] O177[理学—基础数学]