## Differential and Integral Equations

- Differential Integral Equations
- Volume 26, Number 7/8 (2013), 837-844.

### Singular elliptic systems with asymptotically linear nonlinearities

#### Abstract

We prove the existence and nonexistence of positive solutions for the system \begin{equation*} \left\{ \begin{array}{c} -\Delta u_{1}=\mu _{1}f_{1}(u_{2})\ \text{ in }\Omega , \\ -\Delta u_{2}=\mu _{2}f_{2}(u_{1}) \ \text{ in }\Omega , \\ \ \ \ \ \ \ \ u_{1}=u_{2}=0 \ \ \ \ \text{ on }\partial \Omega , \end{array} \right. \end{equation*} where $\Omega $ is a bounded domain in $\mathbb{R}^{n\text{ }}$with smooth boundary $ \partial \Omega ,$ $\mu _{i}$ are positive parameters, and $ f_{i}:(0,\infty )\rightarrow \mathbb{R}$ are asymptotically linear at $ \infty $ and allowed to be singular at $0,$ $i=1,2$.

#### Article information

**Source**

Differential Integral Equations, Volume 26, Number 7/8 (2013), 837-844.

**Dates**

First available in Project Euclid: 20 May 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1369057819

**Mathematical Reviews number (MathSciNet)**

MR3098989

**Zentralblatt MATH identifier**

1299.35100

**Subjects**

Primary: 35J47: Second-order elliptic systems 35J75: Singular elliptic equations

#### Citation

Hai, D.D. Singular elliptic systems with asymptotically linear nonlinearities. Differential Integral Equations 26 (2013), no. 7/8, 837--844. https://projecteuclid.org/euclid.die/1369057819