Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/stability-and-boundedness-criteria-of-solutions-of-a-certain-system-of-L6MrfJb36C
References (50)
-
B. Ogundare, A. Ademola, M. Ogundiran, O. Adesina (2017)
On the qualitative behaviour of solutions to certain second order nonlinear differential equation with delayANNALI DELL'UNIVERSITA' DI FERRARA, 63
-
WS Loud (1957)
Boundedness and convergence of solutions of x�+cx?+g(x)=e(t)\documentclass[12pt]{minimal}Duke Math. J., 24
-
S. العزاوي, Na'mh عبد, Zainab جودة (2015)
Bounded Solutions of the Second Order Differential Equation x ̈+f(x) x ̇+g(x)=u(t)Baghdad Science Journal, 12
-
HOT Tejumola (1969)
On the Boundedness and periodicity of solutions of certain third-order nonlinear differential equationAnn. Math. Pura Appl., 83
-
H. Tejumola (1969)
On the boundedness and periodicity of solutions of certain third-order non-linear differential equationsAnnali di Matematica Pura ed Applicata, 83
-
C. Tunç (2013)
Stability to vector Liénard equation with constant deviating argumentNonlinear Dynamics, 73
-
A. Ademola, B. Ogundare, M. Ogundiran, O. Adesina (2016)
Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential EquationsInternational Journal of Differential Equations, 2016
-
C. Tunç, S. Mohammed (2019)
On the asymptotic analysis of bounded solutions to nonlinear differential equations of second orderAdvances in Difference Equations, 2019
-
R. Bellman (1972)
Introduction to Matrix Analysis -
MO Omeike, AA Adeyanju, DO Adams, AL Olutimo (2021)
Boundedness of certain system of second order differential equationsKragujevac J. Math., 45
-
AA Adeyanju, DO Adams (2021)
Some new results on the stability and boundedness of solutions of certain class of second order vector differential equationsInt. J. Math. Anal. Optim. Theory Appl., 7
-
A. Sadek (2004)
On the stability of a nonhomogeneous vector differential equation of the fourth-orderAppl. Math. Comput., 150
-
J. Graef, A. Baliki, M. Benchohra (2016)
Global existence and stability for second order functional evolution equations with infinite delayElectronic Journal of Qualitative Theory of Differential Equations
-
O. Tunç, C. Tunç (2019)
On the asymptotic stability of solutions of stochastic differential delay equations of second orderJournal of Taibah University for Science, 13
-
J. Ezeilo (1966)
On the existence of almost periodic solutions of some dissipative second order differential equationsAnnali di Matematica Pura ed Applicata, 74
-
C. Tunç, O. Tunç (2015)
On the boundedness and integration of non-oscillatory solutions of certain linear differential equations of second orderJournal of Advanced Research, 7
-
AT Ademola (2015)
Boundedness and stability of solutions to certain second order differential equationsDiffer. Eqs. Control Process., 3
-
Hal Smith (2010)
An introduction to delay differential equations with applications to the life sciences / Hal Smith, 2011
-
M. Eberhart (2016)
Ordinary Differential Equations With Applications -
J. Ezeilo (1966)
On the convergence of solutions of certain systems of second order differential equationsAnnali di Matematica Pura ed Applicata (1923 -), 72
-
A. Adeyanju, D. Adams (2021)
Some new results on the stability and boundedness of solutions of certain class of second order vector differential equationsInternational Journal of Mathematical Analysis and Optimization: Theory and Applications
-
C. Tunç, O. Tunç (2017)
A note on the stability and boundedness of solutions to non-linear differential systems of second orderJournal of the Association of Arab Universities for Basic and Applied Sciences, 24
-
J. Awrejcewicz (2014)
Ordinary Differential Equations and Mechanical Systems -
T. Cemil (2010)
A NOTE ON BOUNDEDNESS OF SOLUTIONS TO A CLASS OF NON-AUTONOMOUS DIFFERENTIAL EQUATIONS OF SECOND ORDERApplicable Analysis and Discrete Mathematics, 4
-
J. Ezeilo (1967)
n-Dimensional extensions of boundedness and stability theorems for some third order differential equationsJournal of Mathematical Analysis and Applications, 18
-
A M A Abou-El-Ela, A I Sadek (1990)
On the stability of solutions for certain second-order stochastic delay differential equationsAnn. Differen. Equat, 6
-
D. Jordan, Peter Smith (2007)
Nonlinear Ordinary Differential Equations: Problems and Solutions: A Sourcebook for Scientists and Engineers -
J Hale (1965)
Sufficient conditions for stability and instability of autonomous functional-differential equationsJ. Differ. Eqs., 1
-
JG Alaba, BS Ogundare (2015)
On stability and boundedness properties of solutions of certain second order non-autonomous non-linear ordinary differential equationKragujevac J. Math., 39
-
(1966)
Stability theory byLiapunov’s secondmethod -
AMA Abou-El-Ela (2015)
1Differ. Eqs. Control Process., 2
-
M. Omeike, O. Oyetunde, A. Olutimo (2014)
Boundedness of Solutions of Certain System of Second-order Ordinary Differential Equations, 53
-
ML Cartwright, JE Littlewood (1947)
On nonlinear differential equations of the second orderAnn. Math., 48
-
J. Hale (1965)
Sufficient conditions for stability and instability of autonomous functional- Differential equations.Journal of Differential Equations, 1
-
AMA Abou-El-Ela, AI Sadek, AM Mahmoud (2015)
On the stability of solutions for certain second-order stochastic delay differential equationsDiffer. Eqs. Control Process., 2
-
MJ Zainab (2015)
Bounded Solution of the Second Order Differential Equation x�+f(x)x?+g(x)=u(t)\documentclass[12pt]{minimal}Baghdad Sci. J., 12
-
AA Adeyanju (2018)
Existence of a limiting regime in the sense of demidovic for a certain class of second order non-linear vector differential equationDiffer. Eq. Control process., 4
-
HOT Tejumola (1971)
Boundedness Criteria for solutions of some second-order differential equationsAtti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur, 50
-
K. Kirsch (2016)
Theory Of Ordinary Differential Equations -
M. Cartwright, J. Littlewood (1947)
On Non-Linear Differential Equations of the Second Order: II. The Equation .. y + kf(y, . y + g(y, k) = p(t) = p 1 (t) + kp 2 (t); k > 0, f(y) > 1Annals of Mathematics, 48
-
A M A Abou-El-Ela (1990)
131Ann. Differen. Equat, 6
-
BS Ogundare, AT Ademola, MO Ogundiran, OA Adesina (2017)
On the qualitative behaviour of solutions to certain second order nonlinear differential equation with delayAnnali dell’Universita’ di Ferrara Sez VII Sci. Mat., 63
-
W. Loud (1957)
Boundedness and convergence of solutions of $x''+cx'+g(x)=e(t)$Duke Mathematical Journal, 24
-
MO Omeike, AA Adeyanju, DO Adams (2018)
Stability and boundedness of solutions of certain vector delay differential equationsJ. Niger. Math. Soc., 37
-
R. Reissig, G. Sansone, R. Conti (1974)
Non-Linear Differential Equations of Higher Order -
C. Tunç (2009)
On the stability and boundedness of solutions of nonlinear vector differential equations of third orderNonlinear Analysis-theory Methods & Applications, 70
-
C Tunc (2005)
Hamdullah Sevli: on the instability of solutions of certain fifth order nonlinear differential equationsMemoirs Differ. Eqs. Math. Phys., 5
-
N. Parke, W. Kaplan (1958)
Ordinary Differential Equations.American Mathematical Monthly, 67
-
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations -
G. Grigoryan (2013)
Boundedness and stability criteria for linear ordinary differential equations of the second orderRussian Mathematics, 57
- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s) under exclusive license to Università degli Studi di Ferrara 2022
- ISSN
- 0430-3202
- eISSN
- 1827-1510
- DOI
- 10.1007/s11565-022-00402-z
- Publisher site
- See Article on Publisher Site
Abstract
This paper provides sufficient conditions for the stability, asymptotic stability, uniform stability, boundedness and uniformly boundedness of solutions of a certain class of second-order nonlinear vector differential equations using the second method of Lyapunov. By constructing a suitable complete Lyapunov function, which serves as a basic tool, we establish the properties mentioned above and thereby improve and complement some known results found in the literature. Lastly, the correctness of our main results is justified by the examples given.
Journal
ANNALI DELL UNIVERSITA DI FERRARA – Springer Journals
Published: May 1, 2023
Keywords: Second order; Stability; Boundedness; Lyapunov function; 34C11; 34C10