Proceedings of the American Mathematical Society

Existence of positive solutions for a semilinear elliptic problem with critical Sobolev and Hardy terms

Author(s): Norimichi Hirano; Naoki Shioji
Journal: Proc. Amer. Math. Soc. 134 (2006), 2585-2592.
MSC (2000): Primary 35J65, 35J20
Posted: February 17, 2006
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Abstract: Let $N\geq4$ , let $2^{\ast}=2N/(N-2)$ and let $\Omega$ $\subset\mathbb{R}^{N}$ be a bounded domain with a smooth boundary $\partial\Omega$ . Our purpose in this paper is to consider the existence of solutions of the problem:

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Norimichi Hirano
Affiliation: Department of Mathematics, Graduate School of Environment and Information Sciences, Yokohama National University, Tokiwadai, Hodogayaku, Yokohama, Japan
Email: hirano@math.sci.ynu.ac.jp

Naoki Shioji
Affiliation: Department of Mathematics, Graduate School of Environment and Information Sciences, Yokohama National University, Tokiwadai, Hodogayaku, Yokohama, Japan

DOI: 10.1090/S0002-9939-06-08405-X
PII: S 0002-9939(06)08405-X
Keywords: Critical Sobolev, Hardy inequality, semilinear elliptic problem
Received by editor(s): August 31, 2004
Received by editor(s) in revised form: March 21, 2005
Posted: February 17, 2006
Additional Notes: This work was partially supported by the Heisei16 joint research project fund in the Graduate School of Environment and Information Sciences of Yokohama National University
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2006, American Mathematical Society

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