On the Existence of Boundary Blow-up Solutions for a General Class of Quasilinear Elliptic Systems

Abstract

Abstract In this paper, we investigate the following quasilinear elliptic system (P) with explosive boundary conditions: Δpu = f1(x, u, v) in Ω; u|∂Ω = +∞, u >0 in Ω, Δqv = f2(x, u, v) in Ω; v|∂Ω = +∞, v >0 in Ω, where Ω is a smooth bounded domain of ℝN, N ≥ 2, 1 < p, q < +∞ and f1, f2 are two Carathéodory functions in Ω × (ℝ+* × ∗ ℝ+*). Under rather general conditions on f1 and f2 and assuming the existence of a sub and supersolutions pair, we prove the existence of a large solution to (P) by a fixed point approach. Then, we apply this result considering particular systems arising in Biology.