Asymptotic behavior of the least-energy solutions of a semilinear elliptic equation with the Hardy-Sobolev critical exponent

详细信息    查看全文

• 作者：Masato Hashizume ^{d15san0f06@st.osaka-cu.ac.jp}
• 关键词：Asymptotic behavior ; Boundary singularity ; Hardy&ndash ; Sobolev inequality ; Minimization problem
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：3107-3131
• 全文大小：343 K
• 卷排序：262

文摘

We investigate the existence, the non-existence and the asymptotic behavior of the least-energy solutions of a semilinear elliptic equation with the Hardy–Sobolev critical exponent. In the boundary singularity case, it is known that the mean curvature of the boundary at origin plays a crucial role on the existence of the least-energy solutions. In this paper, we study the relation between the asymptotic behavior of the solutions and the mean curvature at origin.