Ground state solutions for generalized quasilinear Schrödinger equations

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Asymptotic Analysis Pub Date : 2024-05-02 DOI:10.3233/asy-241913

Xiang-Dong Fang, Zhi-Qing Han

引用次数: 0

Abstract

In this paper we consider the generalized quasilinear Schrödinger equations − div ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) | ∇ u | 2 + V ( x ) u = h ( x , u ) , x ∈ R N , where V and h are periodic in x i , 1 ⩽ i ⩽ N. By using variational methods, we prove the existence of ground state solutions, i.e., nontrivial solutions with least possible energy.

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广义准薛定谔方程的基态解

在本文中，我们考虑广义的准薛定谔方程 - div ( g 2 ( u )∇ u )+ g ( u ) g ′ ( u ) |∇ u | 2 + V ( x ) u = h ( x , u ) , x ∈ R N ，其中 V 和 h 在 x i 中是周期性的，1 ⩽ i ⩽ N。通过使用变分法，我们证明了基态解的存在，即具有最小可能能量的非微分解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Asymptotic Analysis 数学-应用数学

CiteScore

1.90

自引率

7.10%

发文量

审稿时长

6 months

期刊介绍： The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.