Positive Solutions for Nonlinear Dirichlet Problems with Convection

被引：5

作者：

Hu, Shouchuan ^{[1
,2
]}

Papageorgiou, Nikolas S. ^{[3
]}

机构：

[1] Shandong Normal Univ, Coll Math, Jinan, Shandong, Peoples R China

[2] Missouri State Univ, Dept Math, Springfield, MO 65804 USA

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

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2020年 / 82卷 / 02期

关键词：

Convection term; Indefinite drift coefficient; Nonlinear regularity; Nonlinear maximum principle; Truncation; Nonlinear Krein-Rutman theorem; P-LAPLACIAN; ELLIPTIC-EQUATIONS; DEPENDENCE;

D O I：

10.1007/s00245-018-9534-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a nonlinear Dirichlet problem driven by thep-Laplacian, a convection term and a(p - 1)-sublinear perturbation. First we assume that the coefficient in the convection term (drift coefficient) is sign changing. Using the theory of nonlinear operators of monotone type together with suitable truncation and comparison techniques we prove the existence of a positive smooth solution. When the drift coefficient is nonnegative, we are able to relax the conditions on the data of the problem.

引用

页码：451 / 470

页数：20

共 28 条

[1]

[Anonymous], 1997, Handbook of multivalued analysis (theory)

[2] The Ambrosetti-Prodi problem for the p-laplace operator [J].

Arcoya, David ;

Ruiz, David .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2006, 31 (06) :849-865

[3]

Bai Y., 2018, ELECT J DIFFER EQ, V2018, P1

[4] Nonlinear nonhomogeneous Robin problems with dependence on the gradient [J].

Bai, Yunru ;

Gasinski, Leszek ;

Papageorgiou, Nikolaos S. .

BOUNDARY VALUE PROBLEMS, 2018, :1-24

[5] MIXED ELLIPTIC PROBLEMS INVOLVING THE p-LAPLACIAN WITH NONHOMOGENEOUS BOUNDARY CONDITIONS [J].

Bonanno, Gabriele ;

D'Agui, Giuseppina .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (11) :5797-5817

[6] A nonlinear Krein Rutman theorem [J].

Chang, K. C. .

JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2009, 22 (04) :542-554

[7] A p-LAPLACIAN SUPERCRITICAL NEUMANN PROBLEM [J].

Colasuonno, Francesca ;

Noris, Benedetta .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (06) :3025-3057

[8]

De Figueiredo D, 2004, DIFFER INTEGRAL EQU, V17, P119

[9] Positive solutions of quasi-linear elliptic equations with dependence on the gradient [J].

Faraci, F. ;

Motreanu, D. ;

Puglisi, D. .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 54 (01) :525-538

[10] Dirichlet problems for the p-Laplacian with a convection term [J].

Garcia-Melian, Jorge ;

Sabina de Lis, Jose C. ;

Takac, Peter .

REVISTA MATEMATICA COMPLUTENSE, 2017, 30 (02) :313-334

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