一类半线性退化Schrödinger方程的无穷多大能量解的存在性  

Infinitely Many Large Energy Solutions For Semi-Linear Degenerate Schrödinger Equations

作　　者：冉玲 陈尚杰[1,2] 李麟 RAN Ling;CHEN Shangjie;LI Lin(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China;Chongqing Key Laboratory of Social Economy and Applied Statistics,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]经济社会应用统计重庆市重点实验室,重庆400067

出　　处：《西南师范大学学报（自然科学版）》2022年第2期21-26,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：重庆市教育委员会基金项目(KJQN20190081);重庆工商大学基金项目(CTBUZDPTTD201909);重庆工商大学研究生创新型科研项目(yjscxx2021-112-57).

摘　　要：本文运用变分法和Z_(2)-山路定理首次研究了半线性退化Schrödinger方程-Δγu+V(x)u=f(x,u)+μg(x,u)x∈RNu∈S2γ,V(x)(RN)无穷多大能量解的存在性.其中N≥2,Δγ是退化椭圆算子,非线性项f(x,u)在无穷远处满足超线性条件,g(x,u)满足次线性条件.In this paper,we firstly obtained the existence of infinitely many large energy solutions for the following semi-linear degenerate Schrödinger equations in RN by variational methods and Z_(2)-mountain pass theorem:-Δγu+V(x)u=f(x,u)+μg(x,u)x∈RNu∈S2γ,V(x)(RN)where N≥2,Δγis a degenerate elliptic operator,nonlinear term of equation f(x,u)satisfy super-linear condition at infinity,and g(x,u)satisfy the sub-linear condition.

关 键 词：半线性退化椭圆方程 变分法 Z_(2)-山路定理 大能量解 

分 类 号：O176.3[理学—数学]