Existence of positive solutions for a semilinear elliptic problem with critical Sobolev and Hardy terms
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- by Norimichi Hirano and Naoki Shioji PDF
- Proc. Amer. Math. Soc. 134 (2006), 2585-2592 Request permission
Abstract:
Let $N\geq 4$, 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: \[ \left \{ \begin {aligned} -\Delta u - \mu \frac {u}{\vert x\vert ^2} &= \vert u\vert ^{2^\ast -1} && \text {in $\Omega $}, \\ u & > 0 && \text {in $\Omega $},\\ u & = 0 && \text {on $\partial \Omega $}, \end {aligned} \right . \] where $0<\mu <(\frac {N-2}{2})^{2}.$References
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Additional Information
- 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
- Received by editor(s): August 31, 2004
- Received by editor(s) in revised form: March 21, 2005
- Published electronically: 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 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 2585-2592
- MSC (2000): Primary 35J65, 35J20
- DOI: https://doi.org/10.1090/S0002-9939-06-08405-X
- MathSciNet review: 2213736