临界增长(p, q)-拉普拉斯方程的节点解

IF 1.1 4区 数学 Q2 MATHEMATICS, APPLIED
Hongling Pu, Sihua Liang, Shuguan Ji
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引用次数: 0

摘要

在这篇文章中,一个类(p, q)拉普拉斯算子方程的关键增长考虑:−−Δp uΔ问u + (| u p−2 + | | |问−2)u +λϕ| u | q−2 u =μg (u) + | |问∗−2 u, x∈R 3−Δϕu = | | q x∈R 3,在Δξu = div(| |∇uξ−2∇u)是ξ拉普拉斯算符(ξ= p, q), 3 2 & lt;p & lt;问& lt;3, λ和μ为正参数,q * = 3q /(3−q)为Sobolev临界指数。我们利用一种基本的约束最小化技术确定了g在适当条件下节点(即变号)解的存在性、能量估计和收敛性,从而推广了已有的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nodal solutions to ( p , q )-Laplacian equations with critical growth
In this paper, a class of ( p , q )-Laplacian equations with critical growth is taken into consideration: − Δ p u − Δ q u + ( | u | p − 2 + | u | q − 2 ) u + λ ϕ | u | q − 2 u = μ g ( u ) + | u | q ∗ − 2 u , x ∈ R 3 , − Δ ϕ = | u | q , x ∈ R 3 , where Δ ξ u = div ( | ∇ u | ξ − 2 ∇ u ) is the ξ-Laplacian operator ( ξ = p , q ), 3 2 < p < q < 3, λ and μ are positive parameters, q ∗ = 3 q / ( 3 − q ) is the Sobolev critical exponent. We use a primary technique of constrained minimization to determine the existence, energy estimate and convergence property of nodal (that is, sign-changing) solutions under appropriate conditions on g, and thus generalize the existing results.
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来源期刊
Asymptotic Analysis
Asymptotic Analysis 数学-应用数学
CiteScore
1.90
自引率
7.10%
发文量
91
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.
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