Translator Disclaimer
2007 Nonexistence results for classes of elliptic systems
R. Shivaji, Jinglong Ye
Differential Integral Equations 20(8): 927-938 (2007).

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.

Citation

Download Citation

R. Shivaji. Jinglong Ye. "Nonexistence results for classes of elliptic systems." Differential Integral Equations 20 (8) 927 - 938, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1210.35125
MathSciNet: MR2339844

Subjects:
Primary: 34B15
Secondary: 34B18, 35J65

Rights: Copyright © 2007 Khayyam Publishing, Inc.

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.20 • No. 8 • 2007
Back to Top