Keywords
Existence results
Differential equation
Fixed point theorems
Three-point non-homogeneous conditions
How to Cite
Abstract
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.
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