Existence of solution for nonlinear fourth-order three-point boundary value problem

Abstract

abstract:In this paper, we study the existence of solution for the fourth-order three-point boundary value problem having the following formwhere η ∈ (0, 1), α, β ∈ R, f ∈ C([0, 1] × R, R), and f (t, 0) = 0. We give sufficient conditions that allow us to obtain the existence of solution. And by using the LeraySchauder nonlinear alternative we prove the existence of at least one solution of the posed problem. As an application, we also given some examples to illustrate the results obtained.

Some existence results on positive solutions for an iterative second-order boundary-value problem with integral boundary conditions

“…This work is a continuation of the obove montioned works, some other works on positivity and boundary value problems [1,3] and our recent papers on iterative problems (see [5,6]). Our main contribution to this important area is to show that the fixed point theory can be applied successfully to iterative problems with integral boundary conditions.…”

Existence Results for Fourth Order Non-Homogeneous Three-Point Boundary Value Problems

“…Later, these results are improved by Almuthaybiri and Tisdell [13]. In 2020, Bekri and Benaicha [14] dealt with the existence results to the problem (4)…”

Existence of a unique solution for a third-order boundary value problem with nonlocal conditions of integral type

“…The Krasnoselkii fixed point theorem together with two fixed point results of Leggett-Williams type was used in [7] to prove the existence of one or multiple solutions to an nth order two-point boundary value problem. The existence of at least one solution for a fourth-order threepoint boundary value problem using the Leray-Schauder nonlinear alternative was studied in [3]. The existence of a unique solution to a third-order three-point boundary value problem applying the Banach fixed point theorem and fixed point theorem of Maia type given by Rus [16] was investigated in [1].…”