穿孔单位球非线性多谐边值问题

IF 0.6 4区数学 Q3 MATHEMATICS

Complex Variables and Elliptic Equations Pub Date : 2023-10-13 DOI:10.1080/17476933.2023.2266681

Zeineb Ben Yahia, Zagharide Zine El Abidine

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引用次数: 0

摘要

在本文中，我们研究了Rn(n大于或等于3)的穿刺单位球中一类非线性多调和边值问题的正连续解的存在性和渐近行为。我们的论点基于与多谐算子(−Δ)m相关的势理论，其中m是小于n2的正整数，加托类Km,n中的函数性质，Karamata正则变分理论工具和Schauder不动点定理。关键词:正解skato类karamata类green函数schauder不动点定理学科分类:35B4035B0935J3035J40致谢感谢审稿人对本文的认真阅读和宝贵建议。披露声明作者未报告潜在的利益冲突。

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Nonlinear polyharmonic boundary value problems in the punctured unit ball

AbstractIn this paper we investigate the existence and the asymptotic behavior of positive continuous solutions for a class of nonlinear polyharmonic boundary value problems in the punctured unit ball of Rn(n⩾3). Our arguments are based on potential theory associated to the polyharmonic operator (−Δ)m, where m is a positive integer less than n2, properties of functions in the Kato class Km,n, Karamata regular variation theory tools and the Schauder fixed point theorem.Keywords: Positive solutionsKato classKaramata classGreen functionSchauder's fixed point theoremAMS SUBJECT CLASSIFICATIONS: 35B4035B0935J3035J40 AcknowledgementThe authors express their gratitude to the referee for the careful reading of the paper and valuable recommendations.Disclosure statementNo potential conflict of interest was reported by the author(s).

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来源期刊

Complex Variables and Elliptic Equations MATHEMATICS-

CiteScore

2.00

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： Complex Variables and Elliptic Equations is devoted to complex variables and elliptic equations including linear and nonlinear equations and systems, function theoretical methods and applications, functional analytic, topological and variational methods, spectral theory, sub-elliptic and hypoelliptic equations, multivariable complex analysis and analysis on Lie groups, homogeneous spaces and CR-manifolds. The Journal was formally published as Complex Variables Theory and Application.