一类拟线性椭圆方程非平凡广义解的存在性

数学物理学报 ›› 2009, Vol. 29 ›› Issue (3): 727-736.

一类拟线性椭圆方程非平凡广义解的存在性

(长沙理工大学数学与计算科学学院 |长沙 410076)

收稿日期:2007-09-21 修回日期:2008-11-10 出版日期:2009-06-25 发布日期:2009-06-25
基金资助:
国家自然科学基金(10671211)资助

The Existence of Nontrivial Generalized Solution of a Class of Quasilinear Elliptic Equations

(School of Mathematics and Computer Science, Changsha University of Science and Technology, Changsha 410077)

Received:2007-09-21 Revised:2008-11-10 Online:2009-06-25 Published:2009-06-25
Supported by:
国家自然科学基金(10671211)资助

摘要/Abstract

摘要：

该文讨论了下列拟线性椭圆方程的Dirichlet问题在一类Orlicz-Sobolev 空间中非平凡解的存在性

{ -div(a(| u(x)|) u(x))=g(x, u), x ∈ Ω，
u(x)=0, x ∈ ∂Ω.

其中Ω 是 Rⁿ中光滑的有界区域. Φ 和 g 满足一定条件时, 利用推广的山路引理证明了上述Dirichlet 问题存在广义的非平凡解的存在性.

关键词: 拟线性椭圆方程, Orlicz-Sobolev 空间, 推广的山路引理, P.S 条件

Abstract:

In this paper, we study the existence of nontrivial solutions of the following quasilinear elliptic Dirichlet problem in an Orlicz-Sobolev space:

{ -div(a(| u(x)|) u(x))=g(x, u), x ∈ Ω，
u(x)=0, x ∈ ∂Ω.

where Ω is a bounded domain in Rⁿ. Using the generalized mountain pass lemma, we prove, under some conditions on Φ and g, the existence of nontrivial generalized solutions for this problem.

Key words: Quasilinear elliptic equation, Orlicz-Sobolev space, Mountain pass lemma, P.S condition

中图分类号:

王吉安, 邓雪梅. 一类拟线性椭圆方程非平凡广义解的存在性[J]. 数学物理学报, 2009, 29(3): 727-736.

WANG Ji-An, DENG Xue-Mei. The Existence of Nontrivial Generalized Solution of a Class of Quasilinear Elliptic Equations[J]. Acta mathematica scientia,Series A, 2009, 29(3): 727-736.

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