Positive solutions for Dirichlet problems involving the mean curvature operator in Minkowski space

被引：5

作者：

Ma, Ruyun ^{[1
,2
]}

机构：

[1] Xidian Univ, Sch Math & Stat, Xian 710071, Shaanxi, Peoples R China

[2] Northwest Normal Univ, Dept Math, Lanzhou 730070, Gansu, Peoples R China

来源：

MONATSHEFTE FUR MATHEMATIK | 2018年 / 187卷 / 02期

关键词：

Quasilinear differential equation; Positive radial solution; Existence; Leray-Schauder fixed point theorem; Mean curvature operator; Minkowski space; BOUNDARY-VALUE-PROBLEMS; RADIAL SOLUTIONS; HYPERSURFACES; EQUATION; BALL;

D O I：

10.1007/s00605-017-1133-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the existence of classical positive radial solutions to the boundary value problems where b > 0, B(b) = {x. RN : | x| < b}, a : [0, b]. R is a continuous function which may change sign, f : [0,8). R is a continuous function with f (s) > 0 in [0, b], and. > 0 is sufficiently small. Our approach is based on the Leray-Schauder fixed point theorem.

引用

页码：315 / 325

页数：11

共 12 条

[1] SPACELIKE HYPERSURFACES WITH PRESCRIBED BOUNDARY-VALUES AND MEAN-CURVATURE [J].

BARTNIK, R ;

SIMON, L .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 87 (01) :131-152

[2]

Bereanu C, 2009, P AM MATH SOC, V137, P161

[3] Multiple positive radial solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space [J].

Bereanu, Cristian ;

Jebelean, Petru ;

Torres, Pedro J. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 265 (04) :644-659

[4]

Bidaut-Veron M.F., 1997, Differ. Integral Equ., V10, P1003

[5] MAXIMAL SPACE-LIKE HYPERSURFACES IN LORENTZ-MINKOWSKI SPACES [J].

CHENG, SY ;

YAU, ST .

ANNALS OF MATHEMATICS, 1976, 104 (03) :407-419

[6]

Coelho I, 2014, TOPOL METHOD NONL AN, V44, P23

[7] Positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space [J].

Corsato, Chiara ;

Obersnel, Franco ;

Omari, Pierpaolo ;

Rivetti, Sabrina .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 405 (01) :227-239

[8] Positive solutions to a class of elliptic boundary value problems [J].

Hai, DD .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 227 (01) :195-199

[9] Positive solutions of quasilinear boundary value problems [J].

Hai, DD ;

Schmitt, K ;

Shivaji, R .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 217 (02) :672-686

[10] Global structure of radial positive solutions for a prescribed mean curvature problem in a ball [J].

Ma, Ruyun ;

Gao, Hongliang ;

Lu, Yanqiong .

JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 270 (07) :2430-2455

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