Affiliations: Departamento de Análisis Matemático, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, 38271 La Laguna, Spain. E-mails: [email protected], [email protected] | Instituto Universitario de Estudios Avanzados en Física Atomica, Molecular y Fotonica, Facultad de Física, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, 38203 La Laguna, Spain | Departamento de Análisis Matemático, Universidad de Alicante, Ap. correos 99, 03080 Alicante, Spain. E-mail: [email protected]
Note: [] On leave from Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1, (1428), Buenos Aires, Argentina.
Abstract: In this work we discuss existence, uniqueness and asymptotic profiles of positive solutions to the quasilinear problem −Δpu+a(x)up−1=−ur in Ω, |∇u|p−2 ∂u/∂ν=λup−1 on ∂Ω for λ∈R, where r>p−1>0, a∈L∞(Ω). We analyze the existence of solutions in terms of a principal eigenvalue, and determine their asymptotic behavior both when r→p−1 and when r→∞.
Keywords: linear and nonlinear eigenvalue problems, sub- and super-solutions, variational methods
