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

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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.

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Authors and Affiliations

  1. Department of Differential Equations and Applied Mathematics, Gdansk University of Technology, Gdańsk, Poland

    T. Jankowski

  2. Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Gdańsk, Poland

    R. Jankowski

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  1. T. Jankowski
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  2. R. Jankowski
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Correspondence to T. Jankowski.

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Communicated by F.E. Udwadia.

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Jankowski, T., Jankowski, R. Multiple Solutions of Boundary-Value Problems for Fourth-Order Differential Equations with Deviating Arguments. J Optim Theory Appl 146, 105–115 (2010). https://doi.org/10.1007/s10957-010-9658-5

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  • DOI: https://doi.org/10.1007/s10957-010-9658-5

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