A sub-supersolution method for nonlinear elliptic singular systems with natural growth and some applications

Abstract

In this paper we give a sub-supersolution method for nonlinear elliptic singular systems with quadratic gradient whose model system is the following where Ω is a smooth bounded domain of RN (N≥3), β,μ≥0, 0<α,γ<1 and regular f1,f2 functions. Moreover, we apply it to prove existence of solution for some systems, including the classical Lotka-Volterra models with gradient terms. Specifically, we study the competition and the symbiotic Lotka-Volterra systems.