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Three Solutions for a Singular Quasilinear Elliptic Problem

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  14 September 2018

Francesca Faraci  and
George Smyrlis
Francesca Faraci
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania, Italy (ffaraci@dmi.unict.it)
George Smyrlis
Affiliation:
Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece (gsmyrlis@math.ntua.gr)
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Abstract

In the present paper we deal with a quasilinear problem involving a singular term. By combining truncation techniques with variational methods, we prove the existence of three weak solutions. As far as we know, this is the first contribution in this direction in the high-dimensional case.

Keywords

singular quasilinear elliptic problemvariational methodsthree smooth solutions

MSC classification

Primary: 35B25: Singular perturbations
Secondary: 35J60: Nonlinear elliptic equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 1 , February 2019 , pp. 179 - 196
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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