A SOBOLEV-HARDY INEQUALITY WITH APPLICATION TO A NONLINEAR ELLIPTIC EQUATION

• 作者: Wu Yun Xie Chaodong
• 来源期刊: 微分方程年刊：英文版
• 学科: 数学
• 关键词: 椭圆形方程 SOBOLEV-HARDY不等式 临界奇异点 存在性 非平凡解
• 年，卷（期）: 2006,（1）
• 页码范围: 69-74
• 页数: 6页
• 分类号: O175.25

摘要

<正>In this paper, when μ< 1/4, and 2 <q<2(3-σ),0≤<σ≤ 2 we discuss the existence of the solution for a nonlinear elliptic equation by an improved Sobolev-Hardy inequality. We also proved that the constant is optimal in the improved Sobolev-Hardy inequality. We also prove that the problem has no nontrivial solution when |y|<R,μ>0 and q=2(3-σ),the method is coming from the idea of Pohozaev.