A bifurcation problem governed by the boundary condition II
Jorge García-Melián, Julio Daniel Rossi, José C. Sabina de Lis · Proceedings of the London Mathematical Society · 2006
In this work we consider the problem Δu = a(x)up in Ω , ∂ u ∂ ν = λ u on ∂Ω, where Ω is a smooth bounded domain, ν is the outward unit normal to ∂Ω, λ is regarded as a parameter and 0 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.