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Constant-Sign and Nodal Solutions to a Dirichlet Problem with p-Laplacian and Nonlinearity Depending on a Parameter

Published online by Cambridge University Press:  05 September 2013

Salvatore A. Marano  and
Nikolaos S. Papageorgiou
Salvatore A. Marano
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viade A. Doria 6, 95125 Catania, Italy, (marano@dmi.unict.it)
Nikolaos S. Papageorgiou
Affiliation:
Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 15780, Greece
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Abstract

A homogeneous Dirichlet problem with p-Laplacian and reaction term depending on a parameter λ > 0 is investigated. At least five solutions—two negative, two positive and one sign-changing (namely, nodal)—are obtained for all λ sufficiently small by chiefly assuming that the involved non-linearity exhibits a concave-convex growth rate. Proofs combine variational methods with truncation techniques.

Keywords

concave–convex nonlinearitiesp-Laplacianconstant-sign solutionsnodal solutionsconcave–convex nonlinearitiesPrimary 35J2535J92
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 2 , June 2014 , pp. 521 - 532
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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