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一类拟线性椭圆方程非平凡广义解的存在性
  • 期刊名称：数学物理学报(中文版)
  • 时间：0
  • 页码：1-9
  • 语言：中文
  • 分类：O175.25[理学—数学;理学—基础数学]
  • 作者机构：[1]长沙理工大学数学与计算科学学院,长沙410076
  • 相关基金：国家自然科学基金（10671211）资助
  • 相关项目：非线性发展型H-半变分不等式及其应用
作者： 王吉安|邓雪梅|
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, Quasilinear elliptic equation, Orliez-Sobolev space, Mountain pass lemma, P.S condition.
中文摘要：

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，Ω u（x）=0, x ∈δΩ.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.

英文摘要：

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 ∈δΩ where Ω is a bounded domain in R^n. Using the generalized mountain pass lemma, we prove, under some conditions on φ and 9, the existence of nontrivial generalized solutions for this problem.

同期刊论文项目
非线性发展型H-半变分不等式及其应用
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