Positive solutions for nonlinear parametric singular Dirichlet problems

被引：42

作者：

Papageorgiou, Nikolaos S. ^{[1
,2
]}

Radulescu, Vicentiu D. ^{[2
,3
,4
]}

Repovs, Dusan D. ^{[2
,5
,6
]}

机构：

[1] Natl Tech Univ Athens, Dept Math, Zografou Campus, Athens 15780, Greece

[2] Inst Math Phys & Mech, Jadranska 19, Ljubljana 1000, Slovenia

[3] AGH Univ Sci & Technol, Fac Appl Math, Al Mickiewicza 30, PL-30059 Krakow, Poland

[4] Simion Stoilow Romanian Acad, Inst Math, POB 1-764, Bucharest 014700, Romania

[5] Univ Ljubljana, Fac Educ, Ljubljana 1000, Slovenia

[6] Univ Ljubljana, Fac Math & Phys, Ljubljana 1000, Slovenia

来源：

BULLETIN OF MATHEMATICAL SCIENCES | 2019年 / 9卷 / 03期

关键词：

Parametric singular term; (p-1)-linear perturbation; uniform nonresonance; nonlinear regularity theory; truncation; strong comparison principle; bifurcation-type theorem; SOBOLEV;

D O I：

10.1142/S1664360719500115

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a nonlinear parametric Dirichlet problem driven by the p-Laplace differential operator and a reaction which has the competing effects of a parametric singular term and of a Caratheodory perturbation which is (p - 1)-linear near vertical bar infinity. The problem is uniformly nonresonant with respect to the principal eigenvalue of ( -Delta(p), W-0(1,p) (Omega)). We look for positive solutions and prove a bifurcation-type theorem describing in an exact way the dependence of the set of positive solutions on the parameter gimel > 0.

引用

页数：21

共 21 条

[1]

Aizicovici Sergiu, 2008, MATH Z, V196, pvi+, DOI 10.1090/ memo/ 0915

[2]

[Anonymous], 2014, TOPOLOGICAL VARIATIO, DOI DOI 10.1007/978-1-4614-9323-5

[3] ON A SINGULAR NONLINEAR DIRICHLET PROBLEM [J].