A unique solution to a fourth-order three-point boundary value problem

Abstract

In this study, it is aimed to examine the solutions of the following nonlocal boundary value problem y (4) + g(x, y) = 0, x ∈ [c, d], y(c) = y ′ (c) = y ′′(c) = 0, y(d) = λy(ξ). Here, ξ ∈ (c, d), λ ∈ R, g ∈ C([c, d] × R, R) and g(x, 0) ̸= 0. It is concentrated on applications of Green’s function that corresponds to the above problem to derive existence and uniqueness results for the solutions. One example is also given to demonstrate the results.