title: 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
metadata.name: dc.contributor.author
metadata.value: Abduragimov, Gusen Elderkhanovich
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-12-02T13:13:01Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-12-02T13:13:01Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2024-03
metadata.lang: -
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu35.2024.107
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/48042
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Differential Equations and Control Processes;Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: boundary value problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: positive solution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Green's function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: cone
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: operator fixed point index
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: 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
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 24107-jdecp-abduragimov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/48042/1/24107-jdecp-abduragimov.pdf
resources.format: Adobe PDF
resources.size: 230,28 kB