A bifurcation problem governed by the boundary condition i
We deal with positive solutions of Δu = a(x)u p in a bounded smooth domain Ω ⊂ ℝN subject to the boundary condition ∂u/∂ν = λu, λ a parameter, p > 1. We prove that this problem has a unique positive solution if and only if 0 < λ < σ1 where, roughly speaking, σ1 is finite if and...
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Autores principales: | , , |
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Formato: | JOUR |
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Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10219722_v14_n5-6_p499_GarciaMelian |
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Sumario: | We deal with positive solutions of Δu = a(x)u p in a bounded smooth domain Ω ⊂ ℝN subject to the boundary condition ∂u/∂ν = λu, λ a parameter, p > 1. We prove that this problem has a unique positive solution if and only if 0 < λ < σ1 where, roughly speaking, σ1 is finite if and only if | ∂ Ω ∩ {a = 0}| > 0 and coincides with the first eigenvalue of an associated eigenvalue problem. Moreover, we find the limit profile of the solution as λ → σ1. © 2007 Birkhaueser. |
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