Large solutions for a cooperative elliptic system of [formula omitted]-Laplacian equations

Abstract

This paper deals with the quasilinear elliptic systems Δ p u = u a v b , Δ p v = u c v e in a smooth bounded domain Ω ⊂ R N , with the boundary conditions u = v = + ∞ on ∂ Ω . The operator Δ p stands for the p -Laplacian operator defined by Δ p u = div ( | ∇ u | p − 2 ∇ u ) , p > 1 , and the exponents verify a , e > p − 1 , b , c < 0 and ( a − p + 1 ) ( e − p + 1 ) > b c . We prove the existence and uniqueness of the positive solution, and obtain the exact blow-up rate near the boundary of the solution.