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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 $$ \left\{ {\begin{array}{*{20}l} {{ - \Delta u = {\left| x \right|}^{\tau } u^{{2^{ * } - 1 - \varepsilon }} } \hfill} & {{x \in \Omega ,} \hfill} \\ {{u > 0} \hfill} & {{x \in \Omega ,} \hfill} \\ {{u = 0} \hfill} & {{x \in \partial \Omega .} \hfill} \\ \end{array} } \right. $$
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jan 1, 2005
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