## Differential and Integral Equations

- Differential Integral Equations
- Volume 20, Number 8 (2007), 927-938.

### Nonexistence results for classes of elliptic systems

#### Abstract

We consider the system \[ -\Delta u = \lambda f(u,v); \, x \in \Omega \] \[ -\Delta v = \lambda g(u,v); \, x \in \Omega \] \[ u = 0 = v; \, x \in \partial\Omega, \] where $\Omega$ is a ball in $ R^{N}, N \geq 1$ and $\partial\Omega$ is its boundary, $\lambda $ is a positive parameter, and $f$ and $g$ are smooth functions that are negative at the origin (semipositone system) and satisfy certain linear growth conditions at infinity. We establish nonexistence of positive solutions when $\lambda$ is large. Our proofs depend on energy analysis and comparison methods.

#### Article information

**Source**

Differential Integral Equations, Volume 20, Number 8 (2007), 927-938.

**Dates**

First available in Project Euclid: 20 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356039364

**Mathematical Reviews number (MathSciNet)**

MR2339844

**Zentralblatt MATH identifier**

1210.35125

**Subjects**

Primary: 34B15: Nonlinear boundary value problems

Secondary: 34B18: Positive solutions of nonlinear boundary value problems 35J65: Nonlinear boundary value problems for linear elliptic equations

#### Citation

Shivaji, R.; Ye, Jinglong. Nonexistence results for classes of elliptic systems. Differential Integral Equations 20 (2007), no. 8, 927--938. https://projecteuclid.org/euclid.die/1356039364