The existence of ground state solutions for semi-linear degenerate Schrödinger equations with steep potential well

IF 1.1 4区数学 Q1 MATHEMATICS

Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2022-01-01 DOI:10.14232/ejqtde.2022.1.30

Ling Ran, Shang-Jie Chen, Lin Li

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引用次数: 0

Abstract

In this article, we study the following degenerated Schrödinger equations: { − Δ γ u + λ V ( x ) u = f ( x , u ) in R N , u ∈ E λ , where λ > 0 is a parameter, Δ γ is a degenerate elliptic operator, the potential V ( x ) has a potential well with bottom and the nonlinearity f ( x , u ) is either super-linear or sub-linear at infinity in u . The existence of ground state solution be obtained by using the variational methods.

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具有陡势井的半线性退化Schrödinger方程基态解的存在性

在这篇文章中，我们研究了在薛定谔均等的追随者:{ − Δ γ u + λ V ( x ) u = f ( x ,在R N中，u ∈ E λ , 在λ> 0是一个参数,Δ γ是a degenerate elliptic接线员,潜在的V (x)具有潜在的潜力，而非线性f (x, u)在你的无限中都是超线性或次线性的。

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

Electronic Journal of Qualitative Theory of Differential Equations 数学-数学

CiteScore

1.40

自引率

9.10%

发文量

审稿时长

3 months

期刊介绍： The Electronic Journal of Qualitative Theory of Differential Equations (EJQTDE) is a completely open access journal dedicated to bringing you high quality papers on the qualitative theory of differential equations. Papers appearing in EJQTDE are available in PDF format that can be previewed, or downloaded to your computer. The EJQTDE is covered by the Mathematical Reviews, Zentralblatt and Scopus. It is also selected for coverage in Thomson Reuters products and custom information services, which means that its content is indexed in Science Citation Index, Current Contents and Journal Citation Reports. Our journal has an impact factor of 1.827, and the International Standard Serial Number HU ISSN 1417-3875. All topics related to the qualitative theory (stability, periodicity, boundedness, etc.) of differential equations (ODE''s, PDE''s, integral equations, functional differential equations, etc.) and their applications will be considered for publication. Research articles are refereed under the same standards as those used by any journal covered by the Mathematical Reviews or the Zentralblatt (blind peer review). Long papers and proceedings of conferences are accepted as monographs at the discretion of the editors.