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Existence of Solutions for Generalized Nonlinear Fourth-Order Differential Equations

Author

Listed:
  • Salah Benhiouna

    (Department of Mathematics, Ecole Normale Supérieure D’enseignement Technologique (ENSET) de Skikda, Skikda 21001, Algeria)

  • Azzeddine Bellour

    (Laboratory of Applied Mathematics and Didactics, Ecole Normale Supérieure de Constantine, Constantine 25016, Algeria)

  • Reemah Alhuzally

    (Department of Mathematics, Faculty of Science, Al-Baha University, Al-Baha P.O. Box 1988, Saudi Arabia)

  • Ahmad M. Alghamdi

    (Mathematics Department, Faculty of Sciences, Umm Al-Qura University, P.O. Box 14035, Makkah 21955, Saudi Arabia)

Abstract

In this article, we studied the existence of solutions for a more general form of nonlinear fourth-order differential equations by using a new generalization of the Arzelá–Ascoli theorem and Schauder fixed theorem under easier and general conditions. Moreover, we provided some sufficient conditions on the nonlinear function that allowed us to deduce the nonexistence results. Finally, we outlined an example to illustrate our main results.

Suggested Citation

  • Salah Benhiouna & Azzeddine Bellour & Reemah Alhuzally & Ahmad M. Alghamdi, 2024. "Existence of Solutions for Generalized Nonlinear Fourth-Order Differential Equations," Mathematics, MDPI, vol. 12(24), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:4002-:d:1548440
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