Abstract
In this work we consider positive solutions to cooperative elliptic systems of the form -Δu = λu - u2 + buυ, -Δυ = μυ - υ2 + cuυ a bounded smooth domain Ω ⊂ ℝN (λ, μ ∈ ℝ, b, c > 0) which blow up on the boundary ∂Ω, that is u(x), v(x) → ∞ as dist(x, ∂Ω) → 0. We show existence and nonexistence of solutions, and give sufficient conditions for uniqueness. We also provide an exact estimate of the behaviour of the solutions near the boundary in terms of dist(x, ∂Ω).
Received: 2002-10-24
Published Online: 2016-03-10
Published in Print: 2003-05-01
© 2016 by Advanced Nonlinear Studies, Inc.
