✦ LIBER ✦

Hardy–Sobolev inequalities in half-space and some semilinear elliptic equations with singular coefficients

✍ Scribed by Shaowei Chen; Shujie Li

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 342 KB
Volume: 66
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2006.02.032

No coin nor oath required. For personal study only.

✦ Synopsis

We study some semilinear elliptic equations with singular coefficients which relate to some Hardy-Sobolev inequalities. We obtain some existence results for these equations and give a theorem for prescribing the Palais-Smale sequence for these equations. Moreover, we find some interesting connections between these equations and some semilinear elliptic equations in hyperbolic space. Using these connections, we obtain many new results for these equations.

📜 SIMILAR VOLUMES

On a semilinear elliptic equation with s

On a semilinear elliptic equation with singular term and Hardy–Sobolev critical growth

✍ Jianqing Chen 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 175 KB

## 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 Hardy–Sobolev critical growth and singular term by using variation