On a System with Multiple Period Annuli

Anita Kirichuka; Felix Sadyrbaev

doi:10.37394/23203.2025.20.11

On a System with Multiple Period Annuli

Anita Kirichuka
, Felix Sadyrbaev

University of Latvia

Daugavpils University

Research output: Contribution to journal › Article › peer-review

Abstract

We consider two-point boundary value problems for the Hamiltonian system of the form x^′ = f(x, y), y^′ = g(x, y), where f(x, y) and g(x, y) are functions with parameters. We estimate the number of positive and oscillatory solutions for the boundary value problems. Our primary tool is the phase plane analysis combined with evaluations of time map functions. Multiple positive solutions are detected due to multiple period annuli.

Original language	English
Pages (from-to)	92-99
Number of pages	8
Journal	WSEAS Transactions on Systems and Control
Volume	20
DOIs	https://doi.org/10.37394/23203.2025.20.11
Publication status	Published - 2025

Keywords

boundary conditions
Hamiltonian systems
multiple positive solutions
ordinary differential equations
oscillation
period annuli

OECD Field of Science

1.1 Mathematics

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10.37394/23203.2025.20.11

Cite this

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title = "On a System with Multiple Period Annuli",

abstract = "We consider two-point boundary value problems for the Hamiltonian system of the form x′ = f(x, y), y′ = g(x, y), where f(x, y) and g(x, y) are functions with parameters. We estimate the number of positive and oscillatory solutions for the boundary value problems. Our primary tool is the phase plane analysis combined with evaluations of time map functions. Multiple positive solutions are detected due to multiple period annuli.",

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AB - We consider two-point boundary value problems for the Hamiltonian system of the form x′ = f(x, y), y′ = g(x, y), where f(x, y) and g(x, y) are functions with parameters. We estimate the number of positive and oscillatory solutions for the boundary value problems. Our primary tool is the phase plane analysis combined with evaluations of time map functions. Multiple positive solutions are detected due to multiple period annuli.

KW - boundary conditions

KW - Hamiltonian systems

KW - multiple positive solutions

KW - ordinary differential equations

KW - oscillation

KW - period annuli

UR - https://www.scopus.com/pages/publications/105005635722

U2 - 10.37394/23203.2025.20.11

DO - 10.37394/23203.2025.20.11

M3 - Article

SN - 1991-8763

VL - 20

SP - 92

EP - 99

JO - WSEAS Transactions on Systems and Control

JF - WSEAS Transactions on Systems and Control

ER -

On a System with Multiple Period Annuli

Abstract

Keywords

OECD Field of Science

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