指数增长非线性条件下涉及连续势的加（(N, p)）权薛定谔问题的最小能量节点解

IF 1.7 4区数学 Q1 Mathematics

Boundary Value Problems Pub Date : 2024-01-25 DOI:10.1186/s13661-024-01829-3

Sami Baraket, Brahim Dridi, Azedine Grine, Rached Jaidane

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引用次数: 0

摘要

本文旨在研究在 $\mathbb{R}^{N}$ 的单位球 B 中，$N>2$ 的对数加权 $(N,p)$ 拉普拉斯问题是否存在能量最小的非小解。方程的非线性是临界或亚临界增长，这是由加权特鲁丁格-莫泽型不等式引起的。我们的方法基于内哈里集的约束最小化、定量变形 Lemma 和度理论结果。

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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Least energy nodal solutions for a weighted $(N, p)$-Schrödinger problem involving a continuous potential under exponential growth nonlinearity

This article aims to investigate the existence of nontrivial solutions with minimal energy for a logarithmic weighted $(N,p)$ -Laplacian problem in the unit ball B of $\mathbb{R}^{N}$ , $N>2$ . The nonlinearities of the equation are critical or subcritical growth, which is motivated by weighted Trudinger–Moser type inequalities. Our approach is based on constrained minimization within the Nehari set, the quantitative deformation lemma, and degree theory results.

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来源期刊

Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

4 months

期刊介绍： The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.