A bifurcation problem governed by the boundary condition II
In this work we consider the problem Δ u = a(x)up in Ω, ∂u/∂v = λu on Ω Ω, where Ω is a smooth bounded domain, v is the outward unit normal to ∂Ω, λ is regarded as a parameter and 0 < p < 1. We consider both cases where a(x) > 0 in Ω or a(x) is allowed to vanish in a whole subdo...
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2007
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00246115_v94_n1_p1_GarciaMelian http://hdl.handle.net/20.500.12110/paper_00246115_v94_n1_p1_GarciaMelian |
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| Sumario: | In this work we consider the problem Δ u = a(x)up in Ω, ∂u/∂v = λu on Ω Ω, where Ω is a smooth bounded domain, v is the outward unit normal to ∂Ω, λ is regarded as a parameter and 0 < p < 1. We consider both cases where a(x) > 0 in Ω or a(x) is allowed to vanish in a whole subdomain Ω0 of Ω. Our main results include existence of non-negative non-trivial solutions in the range 0 < λ < σ1, where σ1 is characterized by means of an eigenvalue problem, uniqueness and bifurcation from infinity of such solutions for small λ, and the appearance of dead cores for large enough λ. © 2006 London Mathematical Society. |
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