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Multiple Boundary Concentrating Solutions to Dirichlet Problem of Hénon Equation

Multiple Boundary Concentrating Solutions to Dirichlet Problem of Hénon Equation Let Ω be the unit ball centered at the origin in $$ \mathbb{R}^{N} {\left( {N \geqslant 4} \right)},2^{ * } = \frac{{2N}} {{N - 2}},\tau > 0,\varepsilon > 0 $$ . We study the following problem $$ \left\{ {\begin{array}{*{20}l} {{ - \Delta u = {\left| x \right|}^{\tau } u^{{2^{ * } - 1 - \varepsilon }} } \hfill} & {{x \in \Omega ,} \hfill} \\ {{u > 0} \hfill} & {{x \in \Omega ,} \hfill} \\ {{u = 0} \hfill} & {{x \in \partial \Omega .} \hfill} \\ \end{array} } \right. $$ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Multiple Boundary Concentrating Solutions to Dirichlet Problem of Hénon Equation

Acta Mathematicae Applicatae Sinica , Volume 22 (1) – Jan 1, 2005

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References (20)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-005-0293-0
Publisher site
See Article on Publisher Site

Abstract

Let Ω be the unit ball centered at the origin in $$ \mathbb{R}^{N} {\left( {N \geqslant 4} \right)},2^{ * } = \frac{{2N}} {{N - 2}},\tau > 0,\varepsilon > 0 $$ . We study the following problem $$ \left\{ {\begin{array}{*{20}l} {{ - \Delta u = {\left| x \right|}^{\tau } u^{{2^{ * } - 1 - \varepsilon }} } \hfill} & {{x \in \Omega ,} \hfill} \\ {{u > 0} \hfill} & {{x \in \Omega ,} \hfill} \\ {{u = 0} \hfill} & {{x \in \partial \Omega .} \hfill} \\ \end{array} } \right. $$

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2005

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