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Multiple Solutions of Boundary-Value Problems for Fourth-Order Differential Equations with Deviating Arguments

  • T. Jankowski
  • R. Jankowski
Article

Abstract

This paper considers fourth-order differential equations with four-point boundary conditions and deviating arguments. We establish sufficient conditions under which such boundary-value problems have positive solutions. We discuss such problems in the cases when the deviating arguments are delayed or advanced. In order to obtain the existence of at least three positive solutions, we use a fixed-point theorem due to Avery and Peterson. To the authors’ knowledge, this is a first paper where the existence of positive solutions of boundary-value problems for fourth-order differential equations with deviating arguments is discussed.

Keywords

Fourth-order differential equations Existence of positive solutions Boundary conditions Advanced and delayed arguments 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Differential Equations and Applied MathematicsGdansk University of TechnologyGdańskPoland
  2. 2.Faculty of Civil and Environmental EngineeringGdansk University of TechnologyGdańskPoland

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