一类拟线性薛定谔方程解的存在性  

Existence of Solutions for a Class of Quasilinear Schrodinger Equation

作　　者：周梦云 蓝永艺[1] ZHOU Mengyun;LAN Yongyi(School of Science,Jimei University,Xiamen 361021,China)

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《集美大学学报（自然科学版）》2024年第4期365-369,共5页Journal of Jimei University：Natural Science

基　　金：福建省自然科学基金项目“奇异Kirchhoff型方程的解及相关问题研究”(2022J01339)。

摘　　要：在R^(N)上探究形式为-Δu+V(x)u-Δ(u^(2))u=h(u)的拟线性薛定谔方程解的存在性,其中N≥3,V:R^(N)→R,h:R→R。运用变分法和山路引理,证明了当函数V和非线性项h分别满足一些适当条件时,该拟线性薛定谔方程存在一个非平凡正解。The existence of the quasilinear Schr dinger equation in R^(N) of the form-Δu+V(x)u-Δ(u^(2))u=h(u),where N≥3,V:R^(N)→R,and h:R→R were functions.Using variational method and mountain pass lemma,it was proved that the quasilinear Schrodinger equation had a nontrivial positive solution when the function V and the nonlinear term h satisfy some appropriate conditions,respectively.

关 键 词：拟线性薛定谔方程 变分法 山路引理 正解 

分 类 号：O177.91[理学—数学]