Elliptic inequalities with nonlinear convolution and Hardy terms in cone-like domains

被引：0

作者：

Ghergu, Marius ^{[1
,2
]}

Yu, Zhe ^{[1
]}

机构：

[1] Univ Coll Dublin, Sch Math & Stat, Dublin, Ireland

[2] Romanian Acad, Inst Math Sim Stoilow, 21 Calea Grivitei St, Bucharest 010702, Romania

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 526卷 / 01期

关键词：

Semilinear elliptic inequalities; Hardy terms; Nonlinear convolution term; Cone-like domains; A priori estimates; POSITIVE SOLUTIONS; WAVE MECHANICS; EQUATIONS; NONEXISTENCE; ATOM;

D O I：

10.1016/j.jmaa.2023.127329

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the inequality -Delta u - mu|x|2u > (|x|-alpha * up)uq in an unbounded cone C rho omega subset of RN (N > 2) generated by a subdomain omega of the unit sphere SN-1 subset of RN, p, q, rho > 0, mu E R and 0 < alpha < N. In the above, |x|-alpha * up denotes the standard convolution operator in the cone C rho omega. We discuss the existence and nonexistence of positive solutions in terms of N, p, q, alpha, mu and omega. Extensions to systems of inequalities are also investigated.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

引用

页数：21

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