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Best Sobolev constants and quasi-linear elliptic equations with critical growth on spheres

✍ Scribed by C. Bandle; L. A. Peletier; S. Stingelin

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 233 KB
Volume: 278
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200410312

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✦ Synopsis

Abstract

Sharp existence and nonexistence results for positive solutions of quasilinear elliptic equations with critical growth in geodesic balls on spheres are established. The arguments are based on Pohozaev type identities and asymptotic estimates for Emden–Fowler type equations. By means of spherical symmetrization and the concentration‐compactness principle existence and nonexistence results for general domains on spheres are obtained. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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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