具有FUCHSIAN势的p- laplace型椭圆方程的正LIOUVILLE定理和渐近性

Q4 Mathematics

Confluentes Mathematici Pub Date : 2010-03-29 DOI:10.1142/S1793744211000321

M. Fraas, Y. Pinchover

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引用次数: 22

摘要

研究了形式为-Δp(u) + V|u|p-2 u = 0的p- laplace型椭圆型方程的正Liouville定理和正解的渐近性，其中X是一个定义域，d≥2且1 < p <∞。我们假设势能V在点ζ处有一个富克斯奇点，其中ζ =∞并且X是截断的c2锥，或者ζ = 0并且ζ是∂X的一个孤立点或者属于∂X的一个c2部分。

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POSITIVE LIOUVILLE THEOREMS AND ASYMPTOTIC BEHAVIOR FOR p-LAPLACIAN TYPE ELLIPTIC EQUATIONS WITH A FUCHSIAN POTENTIAL

We study positive Liouville theorems and the asymptotic behavior of positive solutions of p-Laplacian type elliptic equations of the form -Δp(u) + V|u|p-2 u = 0 in X, where X is a domain in ℝd, d ≥ 2 and 1 < p < ∞. We assume that the potential V has a Fuchsian type singularity at a point ζ, where either ζ = ∞ and X is a truncated C2-cone, or ζ = 0 and ζ is either an isolated point of ∂X or belongs to a C2-portion of ∂X.

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来源期刊

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.