Article ID Journal Published Year Pages File Type
841384 Nonlinear Analysis: Theory, Methods & Applications 2010 8 Pages PDF
Abstract

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 Δpu=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)>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.

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