On Solutions of a Boundary Value Problem for a Second-Order Differential Equation with a Parameter and Discontinuous Right-Hand Side

O. V. Baskov; Басков О. В.; D. K. Potapov; Потапов Д. К.

doi:10.31857/S0044466923080021

On Solutions of a Boundary Value Problem for a Second-Order Differential Equation with a Parameter and Discontinuous Right-Hand Side

Authors: Baskov O.V.¹, Potapov D.K.¹
Affiliations:
1. St. Petersburg State University
Issue: Vol 63, No 8 (2023)
Pages: 1296-1308
Section: Ordinary differential equations
URL: https://freezetech.ru/0044-4669/article/view/664996
DOI: https://doi.org/10.31857/S0044466923080021
EDN: https://elibrary.ru/IIAYWK
ID: 664996

Cite item

Full Text

Open Access
Restricted Access

Access granted
Restricted Access

Subscription Access

Abstract

A boundary value problem for a second-order ordinary differential equation with a parameter and discontinuous right-hand side is considered. Theorems on the number of solutions to the problem are established. The resulting solutions are illustrated by plots. The process of numerically solving the problem is described.

Keywords

boundary value problem, ordinary differential equation, discontinuous right-hand side, analytical solution, numerical solution

About the authors

O. V. Baskov

St. Petersburg State University

Email: d.potapov@spbu.ru
199034, St. Petersburg, Russia

D. K. Potapov

St. Petersburg State University

Author for correspondence.
Email: d.potapov@spbu.ru
199034, St. Petersburg, Russia

References

Потапов Д.К. Задача Штурма–Лиувилля с разрывной нелинейностью // Дифференц. ур-ния. 2014. Т. 50. № 9. С. 1284–1286.
Kamachkin A.M., Potapov D.K., Yevstafyeva V.V. Solution to second-order differential equations with discontinuous right-hand side // Electron. J. Differ. Equat. 2014. № 221. P. 1–6.
Llibre J., Teixeira M.A. Periodic solutions of discontinuous second order differential systems // J. Singularities. 2014. V. 10. P. 183–190.
Потапов Д.К. Существование решений, оценки дифференциального оператора и “разделяющее” множество в краевой задаче для дифференциального уравнения второго порядка с разрывной нелинейностью // Дифференц. ур-ния. 2015. Т. 51. № 7. С. 970–974.
Самойленко А.М., Нижник И.Л. Дифференциальные уравнения с биустойчивой нелинейностью // Укр. матем. ж. 2015. Т. 67. № 4. С. 517–554.
Bonanno G., D’Agui G., Winkert P. Sturm–Liouville equations involving discontinuous nonlinearities // Minimax Theory Appl. 2016. V. 1. № 1. P. 125–143.
Kamachkin A.M., Potapov D.K., Yevstafyeva V.V. Non-existence of periodic solutions to non-autonomous second-order differential equation with discontinuous nonlinearity // Electron. J. Differ. Equat. 2016. № 04. P. 1–8.
Kamachkin A.M., Potapov D.K., Yevstafyeva V.V. Existence of solutions for second-order differential equations with discontinuous right-hand side // Electron. J. Differ. Equat. 2016. № 124. P. 1–9.
Bensid S., Diaz J.I. Stability results for discontinuous nonlinear elliptic and parabolic problems with a S-shaped bifurcation branch of stationary solutions // Disc. Contin. Dyn. Syst. Ser. B. 2017. V. 22. № 5. P. 1757–1778.
da Silva C.E.L., da Silva P.R., Jacquemard A. Sliding solutions of second-order differential equations with discontinuous right-hand side // Math. Meth. Appl. Sci. 2017. V. 40. № 14. P. 5295–5306.
Павленко В.Н., Постникова Е.Ю. Задача Штурма–Лиувилля для уравнения с разрывной нелинейностью // Челяб. физ.-матем. ж. 2019. Т. 4. Вып. 2. С. 142–154.
da Silva C.E.L., Jacquemard A., Teixeira M.A. Periodic solutions of a class of non-autonomous discontinuous second-order differential equations // J. Dyn. Contr. Syst. 2020. V. 26. № 1. P. 17–44.
Калиткин Н.Н. Численные методы. М.: Наука, 1978.