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

Abstract

The present paper focuses on establishing the existence and uniqueness of solutions to the nonlinear differential equations of order four y⁽⁴⁾(t) + g(t, y(t)) = 0, t ∈ [a, b], together with the non-homogeneous three-point boundary conditions y(a) = 0, y′(a) = 0, y′′(a) = 0, y(b) − αy(ξ ) = λ, where 0 ≤ a < b, ξ ∈ (a, b), α, λ are real numbers and the function g: [a, b] × R→R is a continuous with g(t, 0) ≠ 0. With the aid of an estimate on the integral of kernel, the existence results to the problem are proved by employing fixed point theorem due to Banach.