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On the Solvability of Fourth-Order Two-Point Boundary Value Problems

Author

Listed:
  • Ravi P. Agarwal

    (Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USA)

  • Petio S. Kelevedjiev

    (Department of Mathematics, Technical University of Sliven, 8800 Sliven, Bulgaria)

Abstract

In this paper, we study the solvability of various two-point boundary value problems for x ( 4 ) = f ( t , x , x ′ , x ″ , x ‴ ) , t ∈ ( 0 , 1 ) , where f may be defined and continuous on a suitable bounded subset of its domain. Imposing barrier strips type conditions, we give results guaranteeing not only positive solutions, but also monotonic ones and such with suitable curvature.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:603-:d:346093
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    References listed on IDEAS

    as
    1. Imed Bachar & Habib Mâagli & Hassan Eltayeb, 2019. "Existence and Iterative Method for Some Riemann Fractional Nonlinear Boundary Value Problems," Mathematics, MDPI, vol. 7(10), pages 1-15, October.
    2. 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.
    3. C. De Coster & C. Fabry & F. Munyamarere, 1994. "Nonresonance conditions for fourth order nonlinear boundary value problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 17, pages 1-16, January.
    4. M. B. M. Elgindi & Zhengyuan Guan, 1997. "On the global solvability of a class of fourth-order nonlinear boundary value problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 20, pages 1-5, January.
    5. Ruyun Ma, 2000. "Existence and uniqueness theorems for some fourth-order nonlinear boundary value problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 23, pages 1-6, January.
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