The Sub-Supersolution Method and Extremal Solutions of Quasilinear Elliptic Equations in Orlicz-Sobolev Spaces

被引：5
|
作者：
Dong, Ge [1 ]
Fang, Xiaochun [2 ]
机构：
[1] Shanghai Jian Qiao Univ, Coll Informat Technol, Shanghai 201306, Peoples R China
[2] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China
来源：
JOURNAL OF FUNCTION SPACES | 2018年 / 2018卷
基金：
中国国家自然科学基金;
关键词：
PARTIAL-DIFFERENTIAL SYSTEMS; WEAK SOLUTIONS; VARIATIONAL-INEQUALITIES; EXISTENCE THEOREM; OPERATORS;
D O I：
10.1155/2018/8104901
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove the existence of extremal solutions of the following quasilinear elliptic problem - Sigma(N)(i=1) (partial derivative/partial derivative(i))a(i)u(x,u)(x), Du(x)) + g(x, u(x), Du(x)) = 0 under Dirichlet boundary condition in Orlicz-Sobolev spaces W0LM(Omega) and give the enclosure of solutions. The differential part is driven by a Leray-Lions operator in Orlicz-Sobolev spaces, while the nonlinear term g : Omega x R x R-N -> R is a Caratheodory function satisfying a growth condition. Our approach relies on the method of linear functional analysis theory and the sub-supersolution method.
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收藏
页数：7
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