## Differential and Integral Equations

### 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

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

Mathematical Reviews number (MathSciNet)
MR2339844

Zentralblatt MATH identifier
1210.35125

#### 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