二阶变非线性指数椭圆型拟线性方程在无界锥型区域上的Dirichlet问题

IF 1.1 4区数学 Q1 MATHEMATICS Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2023-01-01 DOI:10.14232/ejqtde.2023.1.33

M. Borsuk, Damian Wiśniewski

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引用次数: 0

摘要

本文研究了一类无界锥型区域上具有m (x)-拉普拉斯算子和右侧强非线性的拟线性二阶椭圆方程的Dirichlet问题。研究了该问题在无穷远处的弱解的性质，得到了解的递减率的急剧指数。我们证明了指数与单位球上Laplace-Beltrami算子的特征值问题的最小特征值有关。

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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The Dirichlet problem in an unbounded cone-like domain for second order elliptic quasilinear equations with variable nonlinearity exponent

In this paper we consider the Dirichlet problem for quasi-linear second-order elliptic equation with the m ( x ) -Laplacian and the strong nonlinearity on the right side in an unbounded cone-like domain. We study the behavior of weak solutions to the problem at infinity and we find the sharp exponent of the solution decreasing rate. We show that the exponent is related to the least eigenvalue of the eigenvalue problem for the Laplace–Beltrami operator on the unit sphere.

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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.