EXISTENCE OF A COOPERATIVE ELLIPTIC SYSTEM INVOLVING PUCCI OPERATOR

doi:10.1016/S0252-9602(10)60030-6

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (1): 137-147.doi: 10.1016/S0252-9602(10)60030-6

EXISTENCE OF A COOPERATIVE ELLIPTIC SYSTEM INVOLVING PUCCI OPERATOR

杨健夫, 余小辉

Department of Mathematics, Jiangxi Normal University, Nanchang 330022, China

收稿日期:2007-07-28 修回日期:2007-09-17 出版日期:2010-01-20 发布日期:2010-01-20
基金资助:
This work is supported by National Natural Sciences Foundations of China (10571175, 10631030).

EXISTENCE OF A COOPERATIVE ELLIPTIC SYSTEM INVOLVING PUCCI OPERATOR

Yang-Jian-Fu, YU Xiao-Hui

Department of Mathematics, Jiangxi Normal University, Nanchang 330022, China

Received:2007-07-28 Revised:2007-09-17 Online:2010-01-20 Published:2010-01-20
Supported by:
This work is supported by National Natural Sciences Foundations of China (10571175, 10631030).

摘要/Abstract

摘要：

The authors study the existence of solutions for the nonlinear elliptic system

{ -M\⁺_λ, ∧(D²u)=f(u, v) in Ω,

-M\⁺_λ, ∧(D²v)=f(u, v) in Ω,

u ≥ 0, v ≥ 0 in Ω,

u=v=0 on ∂Ω,

where Ω is a bounded convex domain in R^N, N ≥ 2. It is shown that under some assumptions on f and g, the problem has at least one positive solution (u,v).

关键词: fixed point index, nonlinear elliptic system, Pucci operator

Abstract:

The authors study the existence of solutions for the nonlinear elliptic system

{ -M\⁺_λ, ∧(D²u)=f(u, v) in Ω,

-M\⁺_λ, ∧(D²v)=f(u, v) in Ω,

u ≥ 0, v ≥ 0 in Ω,

u=v=0 on ∂Ω,

where Ω is a bounded convex domain in R^N, N ≥ 2. It is shown that under some assumptions on f and g, the problem has at least one positive solution (u,v).

Key words: fixed point index, nonlinear elliptic system, Pucci operator

中图分类号:

35J50

杨健夫, 余小辉. EXISTENCE OF A COOPERATIVE ELLIPTIC SYSTEM INVOLVING PUCCI OPERATOR[J]. 数学物理学报(英文版), 2010, 30(1): 137-147.

Yang-Jian-Fu, YU Xiao-Hui. EXISTENCE OF A COOPERATIVE ELLIPTIC SYSTEM INVOLVING PUCCI OPERATOR[J]. Acta mathematica scientia,Series B, 2010, 30(1): 137-147.

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EXISTENCE OF A COOPERATIVE ELLIPTIC SYSTEM INVOLVING PUCCI OPERATOR

EXISTENCE OF A COOPERATIVE ELLIPTIC SYSTEM INVOLVING PUCCI OPERATOR

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