Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

On the Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for One Nonlinear Functional - Differential Equation of Even Order

Author(s):

Gusen Elderkhanovich Abduragimov

Candidate of Physical and Mathematical Sciences, Associate Professor,
Department of Applied Mathematics, Dagestan State University (DSU)

gusen_e@mail.ru

Abstract:

In this article, we consider a two-point boundary value problem for one nonlinear functional differential equation of even order with strong non-linearity on segment [0,1] with homogeneous boundary conditions. With the use of special topological means, sufficient conditions for the existence and uniqueness of a positive solution to the problem under consideration. Existence of a positive solution proved using the well-known Krasnoselsky theorem on a fixed point in a cone, uniqueness is respectively established using the contraction mapping principle. A non-trivial example is given, illustrating the fulfillment of sufficient conditions unique solvability of the problem.

Keywords

• boundary value problem
• cone
• Green's function
• positive solution

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