Nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary |
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| Authors: | J García-Melián C Morales-Rodrigo J D Rossi A Suárez |
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| Institution: | (1) Dpto. de Análisis Matemático, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, 38271 La Laguna, Spain;(2) Dpto. de Ecuaciones Diferenciales y Análisis Numérico Fac. de Matemáticas, Univ. de Sevilla, C/. Tarfia s/n, 41012 Sevilla, Spain;(3) Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina;(4) Instituto de Matemáticas y Física Fundamental, CSIC, C/. Serrano 123, 28006 Madrid, Spain |
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| Abstract: | In this paper we perform an extensive study of the existence, uniqueness (or multiplicity) and stability of nonnegative solutions
to the semilinear elliptic equation − Δu = λ u − u
p
in Ω, with the nonlinear boundary condition ∂u/∂ν = u
r
on ∂Ω. Here Ω is a smooth bounded domain of  with outward unit normal ν, λ is a real parameter and p, r > 0. We also give the precise behavior of solutions for large |λ| in the cases where they exist. The proofs are mainly
based on bifurcation techniques, sub-supersolutions and variational methods.
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| Keywords: | Elliptic equations Nonlinear boundary conditions |
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