一类非线性椭圆不等式Liouville性质的尖锐条件

IF 0.4 4区数学 Q4 MATHEMATICS

Colloquium Mathematicum Pub Date : 2021-01-01 DOI:10.4064/cm8147-1-2020

P. Souplet

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引用次数: 1

摘要

．研究了抛物型问题爆破率估计中出现的一类椭圆型不等式，得到了一个尖锐的存在/不存在性结果。即，对于任意p≥1，我们证明了当且仅当n≥2时，不等式∆u + u p≤ε在R n中，u(0) = 1有一个径向的，正的非递增解。这解决了[Souplet & Tayachi, Colloq. Math. 88(2001)]中留下的一个问题。结果与经典情况ε = 0相反。

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Sharp condition for the Liouville property in a class of nonlinear elliptic inequalities

. We study a class of elliptic inequalities which arise in the study of blow-up rate estimates for parabolic problems, and obtain a sharp existence/nonexistence result. Namely, for any p ≥ 1 , we show that the inequality ∆u + u p ≤ ε in R n with u (0) = 1 admits a radial, positive nonincreasing solution for all ε > 0 if and only if n ≥ 2 . This solves a problem left open in [Souplet & Tayachi, Colloq. Math. 88 (2001)]. The result stands in contrast with the classical case ε = 0 .

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来源期刊

Colloquium Mathematicum MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Colloquium Mathematicum is a journal devoted to the publication of original papers of moderate length addressed to a broad mathematical audience. It publishes results of original research, interesting new proofs of important theorems and research-expository papers in all fields of pure mathematics. Two issues constitute a volume, and at least four volumes are published each year.