Large Solutions for an Elliptic System of Quasilinear Equations
نویسندگان
چکیده
In this paper we consider the quasilinear elliptic system ∆pu = uv, ∆pv = uv in a smooth bounded domain Ω ⊂ R , with the boundary conditions u = v = +∞ on ∂Ω. The operator ∆p stands for the p-Laplacian defined by ∆pu = 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. We analyze positive solutions in both components, providing necessary and sufficient conditions for existence. We also prove uniqueness of positive solutions in the case (a − p + 1)(e − p + 1) > bc and obtain the exact blow-up rate near the boundary of the solution. In the case (a − p + 1)(e − p + 1) = bc, infinitely many positive solutions are constructed.
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