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 is an element of [c,d], y(c) = y'(c) = y ''(c) = 0, y(d) = lambda y(xi). Here, xi is an element of (c, d), lambda is an element of R, g is an element of C ([c, d] x R, R) and g (x , 0) not equal 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.