title: On the Stability and Boundedness of Solutions to Certain Second Order Differential Equation
metadata.name: dc.contributor.author
metadata.value: Adeyanju, Adetunji Adedotun
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Adams, Daniel Oluwasegun
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-10-06T14:17:54Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-10-06T14:17:54Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-09
metadata.lang: -
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu35.2023.304
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/44139
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this paper, we investigate by means of second method of Lyapunov, sufficient conditions that guarantee uniform-asymptotic stability of the trivial solution and ultimate boundedness of all solutions to a certain second order differential equation. We construct a complete Lyapunov function in order to discuss the qualitative properties mentioned earlier. The boundedness result in this paper is new and also complement some boundedness results in literature obtained by using an incomplete Lyapunov function together with a signum function. Finally, we demonstrate the correctness of our results with two numerical examples and graphical representation of the trajectories of solutions to the examples using Maple software.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
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 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: Boundedness
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lyapunov function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Second order
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Stability
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the Stability and Boundedness of Solutions to Certain Second Order Differential Equation
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 59-70.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/44139/1/59-70.pdf
resources.format: Adobe PDF
resources.size: 221,05 kB