Large solutions for a cooperative elliptic system of image-Laplacian equations Original Research Article

This paper deals with the quasilinear elliptic systems Δpu=uavb,Δpv=ucveΔpu=uavb,Δpv=ucve in a smooth bounded domain Ω⊂RNΩ⊂RN, with the boundary conditions u=v=+∞u=v=+∞ on ∂Ω∂Ω. The operator ΔpΔp stands for the pp-Laplacian operator defined by View the MathML sourceΔpu=div(|∇u|p−2∇u),p>1, and the exponents verify View the MathML sourcea,e>p−1,b,c<0 and (a−p+1)(e−p+1)>bc(a−p+1)(e−p+1)>bc. We prove the existence and uniqueness of the positive solution, and obtain the exact blow-up rate near the boundary of the solution.