Quasilinear elliptic systems in divergence form associated to general nonlinearities

Abstract

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 ⊂ ℝ N {\Omega\subset\mathbb{R}^{N}} associated to general continuous nonlinearities satisfying a local assumption near zero. As a consequence, in the case Ω = ℝ N {\Omega=\mathbb{R}^{N}} , we obtain nonexistence theorems of positive solutions. No hypotheses on the solutions at infinity are assumed.