A nonsmooth variational approach to semipositone quasilinear problems in RN

被引：2
|
作者：
Santos, Jefferson Abrantes [1 ]
Alves, Claudianor O. [1 ]
Massa, Eugenio [2 ]
机构：
[1] Univ Fed Campina Grande, Unidade Acad Matemat, BR-58429900 Campina Grande, PB, Brazil
[2] Univ Sao Paulo, Dept Matemat, Inst Ciencias Matemat & Computacao, Campus Sao Carlos, BR-13560970 Sao Carlos, SP, Brazil
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 527卷 / 01期
关键词：
Semipositone problems; Quasilinear elliptic equations; Nonsmooth variational methods; Lipschitz functional; Positive solutions; POSITIVE SOLUTIONS; REGULARITY; EXISTENCE;
D O I：
10.1016/j.jmaa.2023.127432
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper concerns the existence of a solution for the following class of semipositone quasilinear problems { -& UDelta;pu = h(x)(f (u) - a) in RN, u > 0 in RN, where 1 < p < N, a > 0, f : [0, +& INFIN;)-+ [0, +& INFIN;) is a function with subcritical growth , f specialIntscript = 0, while h : RN-+ (0, +& INFIN;) is a continuous function that satisfies some technical conditions. We prove via nonsmooth critical points theory and comparison principle, that a solution exists for a small enough. We also provide a version of Hopf's Lemma and a Liouville-type result for the p -Laplacian in the whole RN.& COPY; 2023 Elsevier Inc. All rights reserved.
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页数：20
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