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

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  • T. Jankowski

    (Gdansk University of Technology)

  • R. Jankowski

    (Gdansk University of Technology)

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.

Suggested Citation

  • T. Jankowski & R. Jankowski, 2010. "Multiple Solutions of Boundary-Value Problems for Fourth-Order Differential Equations with Deviating Arguments," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 105-115, July.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:1:d:10.1007_s10957-010-9658-5
    DOI: 10.1007/s10957-010-9658-5
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    Cited by:

    1. Kun Wang & Zhilin Yang, 2013. "Positive Solutions for a Fourth-Order Boundary Value Problem," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, January.

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