The Unique Solution to the Differential Equations of the Fourth Order with Non-Homogeneous Boundary Conditions
DOI:
https://doi.org/10.15377/2409-5761.2022.09.15Keywords:
Kernel, Existence results, Differential equation, Fixed point theorems, Three-point non-homogeneous conditionsAbstract
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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