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Two non-trivial solutions for a non-homogeneous Neumann problem: an Orlicz–Sobolev space setting

Published online by Cambridge University Press:  25 March 2009

Alexandru Kristály ,
Mihai Mihăilescu  and
Vicenţiu Rădulescu
Alexandru Kristály
Affiliation:
Department of Economics, University of Babeş-Bolyai, 400591 Cluj-Napoca, Romania and Department of Mathematics, Central European University, 1051 Budapest, Hungary (alexandrukristaly@yahoo.com)
Mihai Mihăilescu
Affiliation:
Department of Mathematics, Central European University, 1051 Budapest, Hungary and Department of Mathematics, University of Craiova, 200585 Craiova, Romania (mmihailes@yahoo.com)
Vicenţiu Rădulescu
Affiliation:
Department of Mathematics, University of Craiova, 200585 Craiova, Romania and Institute of Mathematics ‘Simion Stoilow’ of the Romanian Academy, 014700 Bucharest, Romania (vicentiu.radulescu@math.cnrs.fr)
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Abstract

In this paper we study a non-homogeneous Neumann-type problem which involves a nonlinearity satisfying a non-standard growth condition. By using a recent variational principle of Ricceri, we establish the existence of at least two non-trivial solutions in an appropriate Orlicz–Sobolev space.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 2 , April 2009 , pp. 367 - 379
Copyright
Copyright © Royal Society of Edinburgh 2009

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