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Open Access Research Article

On a Perturbed Dirichlet Problem for a Nonlocal Differential Equation of Kirchhoff Type

Giovanni Anello

Author Affiliations

Department of Mathematics, University of Messina, S. Agata, 98166 Messina, Italy

Boundary Value Problems 2011, 2011:891430  doi:10.1155/2011/891430

Published: 9 August 2010

Abstract

We study the existence of positive solutions to the following nonlocal boundary value problem in , on , where , is a Carathéodory function, is a positive continuous function, and is a real parameter. Direct variational methods are used. In particular, the proof of the main result is based on a property of the infimum on certain spheres of the energy functional associated to problem in , .