2020

DOI: 10.31926/but.mif.2020.13.62.1.5

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Triple positive solutions for a class of boundary value problems with integral boundary conditions

Slimane Benaicha

¹

,

Noureddine Bouteraa

²

,

³

Abstract: In this paper, by using Leggett-Williams fixed-point theorem and Hölder inequality, we study the existence of three positive solutions for fourth-order differential equations with integral boundary conditions. The results are illustrated with an example.

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Cited by 3 publications

References 26 publications

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A Study of Nonlinear Boundary Value Problem

2022

Simulation Modeling

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In this chapter, firstly we apply the iterative method to establish the existence of the positive solution for a type of nonlinear singular higher-order fractional differential equation with fractional multi-point boundary conditions. Explicit iterative sequences are given to approximate the solutions and the error estimations are also given. Secondly, we cover the multi-valued case of our problem. We investigate it for nonconvex compact valued multifunctions via a fixed point theorem for multivalued maps due to Covitz and Nadler. Two illustrative examples are presented at the end to illustrate the validity of our results.

A Study of Nonlinear Boundary Value Problem

2022

Simulation Modeling

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In this chapter, firstly we apply the iterative method to establish the existence of the positive solution for a type of nonlinear singular higher-order fractional differential equation with fractional multi-point boundary conditions. Explicit iterative sequences are given to approximate the solutions and the error estimations are also given. Secondly, we cover the multi-valued case of our problem. We investigate it for nonconvex compact valued multifunctions via a fixed point theorem for multivalued maps due to Covitz and Nadler. Two illustrative examples are presented at the end to illustrate the validity of our results.

A Study for Coupled Systems of Nonlinear Boundary Value Problem

2023

Boundary Layer Flows - Modelling, Computation, and Applications of Laminar, Turbulent Incompressible and Compressible Flows

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This chapter deals with the existence and uniqueness of solutions for a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions and for the system of two-point boundary value problem when we take the case of integer derivative. The existence results for the fist problem are obtained by using Leray-Shauder nonlinear alternative and Banach contraction principle and for the second problem, we derive explicit eigenvalue intervals of λ for the existence of at least one positive solution by using Krasnosel’skii fixed point theorem. An illustrative examples is presented at the end for each problem to illustrate the validity of our results.

Existence Results for Boundary Value Problem of Nonlinear Fractional Differential Equation

2023

Nonlinear Systems - Recent Developments and Advances

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