Differential and Integral Equations

Nonexistence results for classes of elliptic systems

R. Shivaji and Jinglong Ye

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34B15: Nonlinear boundary value problems
Secondary: 34B18: Positive solutions of nonlinear boundary value problems 35J65: Nonlinear boundary value problems for linear elliptic equations


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.

Export citation