非线性SchroO^¨dinger-Kirchhoff型方程基态解的存在性  

Existence of Ground States Solution of Nonlinear Schro?dinger-Kirchhoff-Type Equation

作　　者：李伟丹 魏公明[1] 

机构地区：[1]上海理工大学理学院,上海

出　　处：《理论数学》2020年第4期330-338,共9页Pure Mathematics

摘　　要：本文利用Nehari流形的方法和Lions引理,将非线性Schro?dinger-Kirchhoff型方程的基态转化为相应能量函的临界点,结合山路引理,证明了该类方程在一定条件下基态解的存在性。In this paper, by using the method of Nehari manifold and Lions lemma, the solutions of nonlinear Schro?dinger-Kirchhoff-type equations are transformed into the critical points of the corresponding energy functional, combined with the mountain pass lemma to prove the existence of ground state solution of this kind of equations under certain conditions.

关 键 词：非线性SchroO style=" margin-left:-10px ">¨dinger-Kirchhoff型方程 Lions引理 Nehari流形 基态解 FATOU引理 

分 类 号：O17[理学—数学]