Existence and nonexistence of radial solutions of the Dirichlet problem for a class of general k-Hessian equations

被引：48

作者：

He, Jianxin ^{[1
]}

Zhang, Xinguang ^{[2
,4
]}

Liu, Lishan ^{[3
,4
]}

Wu, Yonghong ^{[4
]}

机构：

[1] Nanjing Univ Posts & Telecommun, Sch Sci, Nanjing 210023, Jiangsu, Peoples R China

[2] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Shandong, Peoples R China

[3] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

[4] Curtin Univ Technol, Dept Math & Stat, Perth, WA 6845, Australia

来源：

NONLINEAR ANALYSIS-MODELLING AND CONTROL | 2018年 / 23卷 / 04期

基金：

中国国家自然科学基金;

关键词：

k-Hessian equation; existence and nonexistence; multiplicity; radial solutions; FRACTIONAL DIFFERENTIAL-EQUATION; 2ND-ORDER ELLIPTIC-EQUATIONS; SYMMETRIC POSITIVE SOLUTIONS; SYSTEM; UNIQUENESS; EIGENVALUE; MODEL;

D O I：

10.15388/NA.2018.4.2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish the existence and nonexistence of radial solutions of the Dirichlet problem for a class of general k-Hessian equations in a ball. Under some suitable local growth conditions for nonlinearity, several new results are obtained by using the fixed point theorem.

引用

页码：475 / 492

页数：18

共 49 条

[1]

[Anonymous], 1982, Izv. Akad. Nauk SSSR Ser. Mat.

[2]

[Anonymous], ELECT J QUAL THEORY

[3]

[Anonymous], 1985, NONLINEAR FUNCTIONAL

[4] THE DIRICHLET PROBLEM FOR NONLINEAR 2ND-ORDER ELLIPTIC-EQUATIONS .1. MONGE-AMPERE EQUATION [J].

CAFFARELLI, L ;

NIRENBERG, L ;

SPRUCK, J .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1984, 37 (03) :369-402

[5] THE DIRICHLET PROBLEM FOR NONLINEAR 2ND-ORDER ELLIPTIC-EQUATIONS .3. FUNCTIONS OF THE EIGENVALUES OF THE HESSIAN [J].

CAFFARELLI, L ;

NIRENBERG, L ;

SPRUCK, J .

ACTA MATHEMATICA, 1985, 155 (3-4) :261-301

[6] INTERIOR W2,P ESTIMATES FOR SOLUTIONS OF THE MONGE-AMPERE EQUATION [J].

CAFFARELLI, LA .

ANNALS OF MATHEMATICS, 1990, 131 (01) :135-150

[7] Hessian equations on exterior domain [J].

Cao, Xu ;

Bao, Jiguang .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 448 (01) :22-43

[8] The interior gradient estimate of Hessian quotient equations [J].

Chen, Chuanqiang .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (03) :1014-1023

[9]

Covei DP, 2017, ACTA MATH SCI, V37, P47

[10] Fixed point theorems for a class of nonlinear operators in Hilbert spaces and applications [J].

Cui, Yujun ;

Sun, Jingxian .

POSITIVITY, 2011, 15 (03) :455-464

← 1 2 3 4 5 →