## Advances in Differential Equations

- Adv. Differential Equations
- Volume 15, Number 5/6 (2010), 401-436.

### On quasilinear Brezis-Nirenberg type problems with weights

Marta García-Huidobro and Cecilia S. Yarur

#### 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.

#### Article information

**Source**

Adv. Differential Equations, Volume 15, Number 5/6 (2010), 401-436.

**Dates**

First available in Project Euclid: 18 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1355854676

**Mathematical Reviews number (MathSciNet)**

MR2643230

**Zentralblatt MATH identifier**

1209.35055

**Subjects**

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations 35J70: Degenerate elliptic equations 35J20: Variational methods for second-order elliptic equations

#### Citation

García-Huidobro, Marta; Yarur, Cecilia S. On quasilinear Brezis-Nirenberg type problems with weights. Adv. Differential Equations 15 (2010), no. 5/6, 401--436. https://projecteuclid.org/euclid.ade/1355854676