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Uniqueness of Positive Solutions for a Class of Fourth-Order Boundary Value Problems

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  • J. Caballero
  • J. Harjani
  • K. Sadarangani

Abstract

The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fourth-order boundary value problem: 𠑦 ( 4 ) ( 𠑡 ) = 𠑓 ( 𠑡 , 𠑦 ( 𠑡 ) ) , 𠑡 ∈ [ 0 , 1 ] , 𠑦 ( 0 ) = 𠑦 ( 1 ) = 𠑦  ( 0 ) = 𠑦  ( 1 ) = 0 . Moreover, under certain assumptions, we will prove that the above boundary value problem has a unique symmetric positive solution. Finally, we present some examples and we compare our results with the ones obtained in recent papers. Our analysis relies on a fixed point theorem in partially ordered metric spaces.

Suggested Citation

  • J. Caballero & J. Harjani & K. Sadarangani, 2011. "Uniqueness of Positive Solutions for a Class of Fourth-Order Boundary Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-13, May.
    • Handle: RePEc:hin:jnlaaa:543035
    DOI: 10.1155/2011/543035
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    Cited by:

    1. Ravi P. Agarwal & Petio S. Kelevedjiev, 2020. "On the Solvability of Fourth-Order Two-Point Boundary Value Problems," Mathematics, MDPI, vol. 8(4), pages 1-19, April.

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