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),
35d2c4684dcbd14f8c84c995b5dc7d4" title="Click to view the MathML source">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.