Asymptotic behavior for elliptic problems with singular coefficient and nearly critical Sobolev growth
β Scribed by Daomin Cao; Shuangjie Peng
- Publisher
- Springer
- Year
- 2005
- Tongue
- English
- Weight
- 276 KB
- Volume
- 185
- Category
- Article
- ISSN
- 0373-3114
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π SIMILAR VOLUMES
## Abstract In a previous work [6], we got an exact local behavior to the positive solutions of an elliptic equation. With the help of this exact local behavior, we obtain in this paper the existence of solutions of an equation with HardyβSobolev critical growth and singular term by using variation
Let \(\Omega\) be a smooth bounded domain of \(\mathbb{R}^{n}, n \geqslant 3\), and let \(a(x)\) and \(f(x)\) be two smooth functions defined on a neighbourhood of \(\Omega\). First we study the existence of nodal solutions for the equation \(\Delta u+a(x) u=f(x)|u|^{4 /(n-2)} u\) on \(\Omega, u=0\)