Positive solutions for quasilinear elliptic inequalities and systems with nonlocal terms

被引：17

作者：

Ghergu, Marius ^{[1
,2
]}

Karageorgis, Paschalis ^{[3
]}

Singh, Gurpreet ^{[3
]}

机构：

[1] Univ Coll Dublin, Sch Math & Stat, Dublin 4, Ireland

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

[3] Trinity Coll Dublin, Sch Math, Dublin, Ireland

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 268卷 / 10期

关键词：

Quasilinear elliptic inequalities; m-Laplace operator; m-Mean curvature operator; Existence and nonexistence of positive solutions; LIOUVILLE THEOREMS; NONEXISTENCE; EQUATIONS;

D O I：

10.1016/j.jde.2019.11.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the existence and nonexistence of positive solutions for the quasilinear elliptic inequality LAu = div[A(x, u, Du)] > * uP)uq in St, where St C RN, N > 1, is an open set. Here L, stands for the Riesz potential of order a E (0, N), p > 0 and q E R. For a large class of operators LA (which includes the m -Laplace and the m -mean curvature operator) we obtain optimal ranges of exponents p, q and a for which positive solutions exist. Our methods are then extended to quasilinear elliptic systems of inequalities. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：6033 / 6066

页数：34

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