具有陡峭势阱的临界拟线性Schrödinger方程基态解的存在性

IF 2.1 2区数学 Q1 MATHEMATICS

Advanced Nonlinear Studies Pub Date : 2022-01-01 DOI:10.1515/ans-2022-0030

Yan-Fang Xue, Xiao-Jing Zhong, Chunlei Tang

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引用次数: 2

摘要

摘要研究了具有临界指数和陡势阱的拟线性薛定谔方程解的存在性。通过变量的变化，将拟线性方程简化为一个半线性方程，其相关泛函在适当的假设下满足Mountain Pass定理的几何条件。得到了基态解的存在性，并考虑了它的浓度行为。

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Existence of ground state solutions for critical quasilinear Schrödinger equations with steep potential well

Abstract We study the existence of solutions for the quasilinear Schrödinger equation with the critical exponent and steep potential well. By using a change of variables, the quasilinear equations are reduced to a semilinear one, whose associated functionals satisfy the geometric conditions of the Mountain Pass Theorem for suitable assumptions. The existence of a ground state solution is obtained, and its concentration behavior is also considered.

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来源期刊

Advanced Nonlinear Studies 数学-数学

CiteScore

3.00

自引率

5.60%

发文量

审稿时长

12 months

期刊介绍： Advanced Nonlinear Studies is aimed at publishing papers on nonlinear problems, particulalry those involving Differential Equations, Dynamical Systems, and related areas. It will also publish novel and interesting applications of these areas to problems in engineering and the sciences. Papers submitted to this journal must contain original, timely, and significant results. Articles will generally, but not always, be published in the order when the final copies were received.