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May/June 2010 On quasilinear Brezis-Nirenberg type problems with weights
Marta García-Huidobro, Cecilia S. Yarur
Adv. Differential Equations 15(5/6): 401-436 (May/June 2010).

Abstract

In this paper we study Brezis-Nirenberg type results for radial solutions of a quasilinear elliptic equation of the form $$ \begin{cases}-\Delta_pu= \lambda C(|x|)|u|^{p-2}u+ B(|x|) |u|^{q-2}u, \ a.e.\ x\in B_R(0)\subset\mathbb R^N,\ R>0,\\ u=0,\quad \mbox{on }\partial B_R(0), \end{cases} $$ where $\lambda\in\mathbb R$, $q\ge p>1$, $\Delta_pu=\mbox{div}(|\nabla u|^{p-2}\nabla u)$, $B_R(0)$ denotes the ball of radius $R>0$ centered at $0$ in $\mathbb R^N$, and the weights $ B,\ C$ are appropriate positive measurable radially symmetric functions.

Citation

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Marta García-Huidobro. Cecilia S. Yarur. "On quasilinear Brezis-Nirenberg type problems with weights." Adv. Differential Equations 15 (5/6) 401 - 436, May/June 2010.

Information

Published: May/June 2010
First available in Project Euclid: 18 December 2012

zbMATH: 1209.35055
MathSciNet: MR2643230

Subjects:
Primary: 35J20, 35J65, 35J70

Rights: Copyright © 2010 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.15 • No. 5/6 • May/June 2010
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