## Differential and Integral Equations

- Differential Integral Equations
- Volume 26, Number 1/2 (2013), 119-128.

### Multiplicity of solutions for a Dirichlet problem with a singular and a supercritical nonlinearities

David Arcoya and Lucio Boccardo

#### Abstract

For a bounded, open set $\Omega\subset\mathbb{R}^N$ and depending on $\lambda>0$, we study the multiplicity of solutions of \begin{equation*} \begin{cases} u>0 \text{ in }\;\Omega\;, \\ -\div (M(x)\nabla u)=\frac{\lambda}{\;u^\gamma\;}+ u^{p} \text{ in }\;\Omega, \\ u=0 \text{ on }\;\partial\Omega, \end{cases} \end{equation*} where $M(x)$ is a symmetric, bounded, and elliptic matrix and $0 <\gamma <1 <p <\frac{N+2}{N-2}$.

#### Article information

**Source**

Differential Integral Equations, Volume 26, Number 1/2 (2013), 119-128.

**Dates**

First available in Project Euclid: 18 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1355867509

**Mathematical Reviews number (MathSciNet)**

MR3058700

**Zentralblatt MATH identifier**

1289.35098

**Subjects**

Primary: 35J60: Nonlinear elliptic equations 35J20: Variational methods for second-order elliptic equations 35J57: Boundary value problems for second-order elliptic systems

#### Citation

Arcoya, David; Boccardo, Lucio. Multiplicity of solutions for a Dirichlet problem with a singular and a supercritical nonlinearities. Differential Integral Equations 26 (2013), no. 1/2, 119--128. https://projecteuclid.org/euclid.die/1355867509