The Unique Solution to the Differential Equations of the Fourth Order with Non-Homogeneous Boundary Conditions

This research paper aims to establish the uniqueness of the solution to fourth-order nonlinear differential equations v(4)(x) + f (x,v(x)) = 0, x ε [a,b], with non-homogeneous boundary conditions where 0 ≤ a < ζ < b, the constants α, ???? are real numbers and f : [a,b] x R →R  is a continuous function with f (x, 0] ≠ 0. Using the sharper bounds on the integral of the kernel, the uniqueness of the solution to the problem is established based on Banach and Rus fixed point theorems on metric spaces. AMS Subject Classification: 34B15, 34B10.