A semilnear singular problem for the fractional laplacian

被引：2

作者：

Godoy, Tomas ^{[1
]}

机构：

[1] Univ Nacl Cordoba, Fac Matemat Astron & Fis, Ciudad Univ, RA-5000 Cordoba, Argentina

来源：

AIMS MATHEMATICS | 2018年 / 3卷 / 04期

关键词：

singular elliptic problems; positive solutions; fractional Laplacian; sub and supersolutions; ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; DIRICHLET PROBLEM; CONVECTION; BEHAVIOR;

D O I：

10.3934/Math.2018.4.464

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the problem (-Delta)(s) u = -au(-gamma) + lambda h in Omega, u = 0 in R-n \Omega, u > 0 in Omega; where 0 < s < 1; Omega is a bounded domain in R-n with C-1,C-1 boundary, a and h are nonnegative bounded functions, h not equivalent to 0; and lambda > 0 : We prove that if gamma is an element of 2 (0; s) then, for lambda positive and large enough, there exists a weak solution such that c(1)d(Omega)(s) <= u <= c(2)d(Omega)(s) in Omega for some positive constants c(1) and c(2) : A somewhat more general result is also given.

引用

页码：464 / 484

页数：21

共 30 条

[1]

[Anonymous], 2007, Handbook of Differential Equations: Stationary Partial Differential Equations. Handbook of Differential Equations

[2] Singular solutions of a nonlinear elliptic equation in a punctured domain [J].

Bachar, Imed ;

Maagli, Habib ;

Radulescu, Vicentiu D. .

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2017, (94) :1-19

[3] Semilinear problems for the fractional laplacian with a singular nonlinearity [J].

Barrios, Begona ;

De Bonis, Ida ;

Medina, Maria ;

Peral, Ireneo .

OPEN MATHEMATICS, 2015, 13 :390-407

[4] Estimates on Green functions and Poisson kernels for symmetric stable processes [J].

Chen, ZQ ;

Song, RM .

MATHEMATISCHE ANNALEN, 1998, 312 (03) :465-501

[5] Combined effects of asymptotically linear and singular nonlinearities in bifurcation problems of Lane-Emden-Fowler type [J].

Cîrstea, F ;

Ghergu, M ;

Radulescu, V .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2005, 84 (04) :493-508

[6] A GLOBAL ESTIMATE FOR THE GRADIENT IN A SINGULAR ELLIPTIC BOUNDARY-VALUE PROBLEM [J].

DELPINO, MA .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1992, 122 :341-352

[7] Local behavior of fractional p-minimizers [J].

Di Castro, Agnese ;

Kuusi, Tuomo ;

Palatucci, Giampiero .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2016, 33 (05) :1279-1299

[8] Hitchhiker's guide to the fractional Sobolev spaces [J].

Di Nezza, Eleonora ;

Palatucci, Giampiero ;

Valdinoci, Enrico .

BULLETIN DES SCIENCES MATHEMATIQUES, 2012, 136 (05) :521-573

[9] On Very Weak Positive Solutions to Some Semilinear Elliptic Problems With Simultaneous Singular Nonlinear and Spatial Dependence Terms [J].

Diaz, J. I. ;

Hernandez, J. ;

Rakotoson, J. M. .

MILAN JOURNAL OF MATHEMATICS, 2011, 79 (01) :233-245

[10] AN ELLIPTIC EQUATION WITH SINGULAR NONLINEARITY [J].

DIAZ, JI ;

MOREL, JM ;

OSWALD, L .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1987, 12 (12) :1333-1344

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