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ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

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

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On the Existence and Uniqueness of a Positive Solution to a Boundary Value Problem with Symmetric Boundary Conditions for One Nonlinear Fourth-order Ordinary Differential Equation

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:

The paper considers a boundary value problem with symmetric boundary conditions for one nonlinear fourth-order ordinary differential equation on the segment $[0,1]$, which describes the deformation of an elastic beam. Using special topological means in semi-ordered spaces with a cone, based on the fixed point principle, sufficient conditions for the existence and uniqueness of a positive solution to the problem under study are established. The proof of the existence of at least one positive solution to the boundary value problem was carried out using the index of the operator's fixed point. To prove the uniqueness of the solution, the theorem on fixed points of alpha-concave operators - was accordingly used.

Keywords

References:

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