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On a singular semilinear elliptic problem with an asymptotically linear nonlinearity

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  11 December 2015

Giovanni Anello  and
Francesca Faraci
Giovanni Anello
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy (ganello@unime.it)
Francesca Faraci*
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania, Italy (ffaraci@dmi.unict.it)
*
*Corresponding author.
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Extract

In this paper we deal with a singular elliptic problem involving an asymptotically linear nonlinearity and depending on two positive parameters. We investigate the existence, uniqueness and non-existence of the minima of the functional associated with the problem and, by employing a natural and very general definition of a weak solution, we also obtain a bifurcation-type result.

Keywords

singular elliptic equationbifurcation problemglobal minima

MSC classification

Secondary: 35B25: Singular perturbations 35J60: Nonlinear elliptic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 1 , February 2016 , pp. 59 - 77
Copyright
Copyright © The Royal Society of Edinburgh 2016 

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