Quasilinear elliptic systems in divergence form associated to general nonlinearities

Abstract

The paper is concerned with a priori estimates of positive solutions of quasilinear elliptic systems of equations or inequalities in an open set of Ω⊂ℝN{\Omega\subset\mathbb{R}^{N}} associated to general continuous nonlinearities satisfying a local assumption near zero. As a consequence, in the case Ω=ℝN{\Omega=\mathbb{R}^{N}}, we obtain nonexistence theorems of positive solutions. No hypotheses on the solutions at infinity are assumed.

Keywords

• quasilinear elliptic systems
• liouville theorems
• positive solutions
• 35b40
• 35b45
• 35j47
• 35j92