Araştırma Makalesi
Yıl 2023,
Cilt: 6 Sayı: 3-Supplement, 62 - 83, 15.10.2023
Öz
Kaynakça
- A.M.A. Abou-El-Ela, A.I. Sadek, A.M. Mahmoud, E.S. Farghaly, New stability and boundedness results for solutions of a certain third-order nonlinear stochastic diferential equation, Asian Journal of Mathematics and Computer Research, Vol.5, No.1, pp.60-70 (2015).
- A.M.A. Abou-El-Ela, A.I. Sadek, A.M. Mahmoud, On the stability of solution for a certain second-order stochastic delay diferential equations, Diferential equation and control process, No.2, pp.1-13 (2015).
- A.M.A. Abou-El-Ela, A.I. Sadek, A.M. Mahmoud, R.O.A. Taie, On the stochastic stability and boundedness of solution for stochastic delay diferential equations of the second-order, Chinese Journal of Mathematics, pp.1-18 (2015).
- A.M.A. Abou-El-Ela, A.I. Sadek, A.M. Mahmoud, E.S. Farghaly, Stability of solutions for certain third-order nonlinear stochastic delay diferential equation, Ann. of Appl. Math., Vol.31, No.3, pp.253-261 (2015).
- A.M.A. Abou-El-Ela, A.I. Sadek, A.M. Mahmoud et al. Asymptotic stability of solutions for a certain non-autonomous second-order stochastic delay diferential equation, Turkish J. Math., Vol.41, No.3, pp.576-584 (2017).
- A.T. Ademola, S.O. Akindeinde, B.S. Ogundare, M.O. Ogundiran, O.A. Adesina, On the stability and boundedness of solutions to certain second-order nonlinear stochastic delay diferential equations, Journal of the Nigerian Mathematical Society, Vol.38, No.2, pp.185-209 (2019).
- A.T. Ademola, P.O. Arawomo, Stability and ultimate boundedness of solutions to certain third-order diferential equations, Applied Mathematics E-Notes, Vol.10, pp.61-69 (2010).
- A.T. Ademola, P.O. Arawomo, Stability, boundedness and asymptotic behavour of solution of a certain nonlinear diferential equations of the third-order, Kragujevac Journal of Mathematics, Vol.35, No.3, pp.431-445 (2011).
- A.T. Ademola, P.O. Arawomo, O.M. Ogunlaran and E.A. Oyekan, Uniform stability, boundedness and asymptotic behaviour of solutions of some third-order nonlinear delay diferential equations, Di_erential Equations and Control Processes, No.4, pp.43-66 (2013).
- A.T. Ademola, P.O. Arawomo, Uniform Stability and boundedness of solutions of nonlinear delay diferential equations of the third-order, Math. J. Okayama Univ., Vol.55, pp.157-166 (2013).
- A.T. Ademola, S. Moyo, M.O. Ogundiran, P.O. Arawomo, O.A. Adesina, Stability and boundedness of solution to a certain second-order non-autonomous stochastic diferential equation, International Journal of Analysis, (2016).
- A.T. Ademola, B.S. Ogundare, M.O. Ogundiran, O.A. Adesina, Periodicity, stability and boundedness of solutions to certain second-order delay diferential equations, International Journal of Di_erential equations, Article ID 2843709, (2016). A.T. Ademola, Stability and uniqueness of solution to a certain third-order stochastic delay di_erential equations. Diferential Equation and Control Process, No.2, pp.24-50 (2017).
- A.T. Ademola, Existence and uniqueness of a periodic solution to certain thirdorder nonlinear delay diferential equation with multiple deviating arguments, Acta Univ. Sapientiae, Mathematica, Vol.5, No.2, pp.113-131 (2013).
- L. Arnold, Stochastic diferential equations: Theory and applications, John Wiley & Sons, (1974).
- T.A. Burton, Volterra Integral and Diferential Equations, (Mathematics in science and engineering 202) Elsevier, (1983).
- T.A. Burton, Stability and periodic solutions of ordinary and functional diferential equations of Mathematics in Science and Engineering, 178. Academic Press Inc., Orlando, Fla, USA, (1985). E.N. Chukwu, On boundedness of solutions of third-order diferential equations, Ann. Mat. Pura. Appl., Vol.104, No.4, pp.123-149 (1975).
- V. Kolmanovskii, L. Shaiket, Construction of Lyapunov functionals for stochastic hereditary systems. A survey of some recent results, Mathematical and computer modelling, Vol.36, No.6, pp.691-716 (2002).
- C. Lamberto, Asymptotic behaviour and stability problems in ordinary diferential equations, Springer-Verlag Berlin Heidelberg, (1956).
- R. Liu, Y. Raoul, Boundedness and exponential stability of highly nonlinear stochastic diferential equations, Electronic Journal of Diferential Equations, No.143, pp.1{10 (2009).
- A.M. Mahmoud, C. Tunc, Asymptotic stability of solutions for a kind of thirdorder stochastic diferential equation with delays, Miskole Mathematical Note, Vol.20, No.1, pp.381-393 (2019).
- X. Mao, Some contributions to stochastic asymptotic stability and boundedness via multiple Lyapunov functions, Journal of Mathematical Analysis and Applications, Vol.260, pp.325-340 (2001).
- B. Oksendal, Stochastic Diferential Equations: An introduction with applications, springer, (2000).
- B.S. Ogundare, A.T. Ademola, M.O. Ogundiran, O.A. Adesina, On the qualitative behaviour of solutions to certain second-order nonlinear diferential equation with delay. Annalidell Universita di Ferrara, (2016).
- Y.N. Raoul, Boundedness and exponential asymptotic stability in dynamical systems with applications to nonlinear diferential equations with unbounded terms, Advances in Dynamical Systems and Applications, Vol.2, No.1, pp.107-121 (2007).
- A. Rodkina, M. Basin, On delay-dependent stability for a class of nonlinear stochastic delay-diferential equations, Mathematics of Control, Signals, and Systems, Vol.18, No.2, pp.187{197 (2006).
- L. Shaikihet, Lyapunov functional and stability of stochastic functional diferential equations, Springer, International, (2013).
- T. Yoshizawa, Stability theory by Liapunov's second method, The Mathematical Society of Japan, (1966).
SOME QUALITATIVE PROPERTIES OF SOLUTIONS OF CERTAIN NONLINEAR THIRD-ORDER STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAY
Öz
This study considered certain nonlinear third-order stochastic differential equations with delay. The third-order equation is reduced to an equivalent system of first-order differential equations and used to construct the desired complete Lyapunov-Krasovski\v{\i} functional. Standard conditions guaranteeing stability when the forcing term is zero, boundedness of solutions when the forcing term is non-zero, and lastly the existence and uniqueness of solutions are derived. The obtained results indicated that the adopted technique is effective in studying the qualitative behaviour of solutions. The obtained results are not only new but extend the frontier of knowledge of the qualitative behaviour of solutions of nonlinear stochastic differential with delay. Finally, two special cases are given to illustrate the derived theoretical results.
Anahtar Kelimeler
Existence of solution Nonlinear stochastic differential equation Uniform stability Third-order Third-order
Kaynakça
- A.M.A. Abou-El-Ela, A.I. Sadek, A.M. Mahmoud, E.S. Farghaly, New stability and boundedness results for solutions of a certain third-order nonlinear stochastic diferential equation, Asian Journal of Mathematics and Computer Research, Vol.5, No.1, pp.60-70 (2015).
- A.M.A. Abou-El-Ela, A.I. Sadek, A.M. Mahmoud, On the stability of solution for a certain second-order stochastic delay diferential equations, Diferential equation and control process, No.2, pp.1-13 (2015).
- A.M.A. Abou-El-Ela, A.I. Sadek, A.M. Mahmoud, R.O.A. Taie, On the stochastic stability and boundedness of solution for stochastic delay diferential equations of the second-order, Chinese Journal of Mathematics, pp.1-18 (2015).
- A.M.A. Abou-El-Ela, A.I. Sadek, A.M. Mahmoud, E.S. Farghaly, Stability of solutions for certain third-order nonlinear stochastic delay diferential equation, Ann. of Appl. Math., Vol.31, No.3, pp.253-261 (2015).
- A.M.A. Abou-El-Ela, A.I. Sadek, A.M. Mahmoud et al. Asymptotic stability of solutions for a certain non-autonomous second-order stochastic delay diferential equation, Turkish J. Math., Vol.41, No.3, pp.576-584 (2017).
- A.T. Ademola, S.O. Akindeinde, B.S. Ogundare, M.O. Ogundiran, O.A. Adesina, On the stability and boundedness of solutions to certain second-order nonlinear stochastic delay diferential equations, Journal of the Nigerian Mathematical Society, Vol.38, No.2, pp.185-209 (2019).
- A.T. Ademola, P.O. Arawomo, Stability and ultimate boundedness of solutions to certain third-order diferential equations, Applied Mathematics E-Notes, Vol.10, pp.61-69 (2010).
- A.T. Ademola, P.O. Arawomo, Stability, boundedness and asymptotic behavour of solution of a certain nonlinear diferential equations of the third-order, Kragujevac Journal of Mathematics, Vol.35, No.3, pp.431-445 (2011).
- A.T. Ademola, P.O. Arawomo, O.M. Ogunlaran and E.A. Oyekan, Uniform stability, boundedness and asymptotic behaviour of solutions of some third-order nonlinear delay diferential equations, Di_erential Equations and Control Processes, No.4, pp.43-66 (2013).
- A.T. Ademola, P.O. Arawomo, Uniform Stability and boundedness of solutions of nonlinear delay diferential equations of the third-order, Math. J. Okayama Univ., Vol.55, pp.157-166 (2013).
- A.T. Ademola, S. Moyo, M.O. Ogundiran, P.O. Arawomo, O.A. Adesina, Stability and boundedness of solution to a certain second-order non-autonomous stochastic diferential equation, International Journal of Analysis, (2016).
- A.T. Ademola, B.S. Ogundare, M.O. Ogundiran, O.A. Adesina, Periodicity, stability and boundedness of solutions to certain second-order delay diferential equations, International Journal of Di_erential equations, Article ID 2843709, (2016). A.T. Ademola, Stability and uniqueness of solution to a certain third-order stochastic delay di_erential equations. Diferential Equation and Control Process, No.2, pp.24-50 (2017).
- A.T. Ademola, Existence and uniqueness of a periodic solution to certain thirdorder nonlinear delay diferential equation with multiple deviating arguments, Acta Univ. Sapientiae, Mathematica, Vol.5, No.2, pp.113-131 (2013).
- L. Arnold, Stochastic diferential equations: Theory and applications, John Wiley & Sons, (1974).
- T.A. Burton, Volterra Integral and Diferential Equations, (Mathematics in science and engineering 202) Elsevier, (1983).
- T.A. Burton, Stability and periodic solutions of ordinary and functional diferential equations of Mathematics in Science and Engineering, 178. Academic Press Inc., Orlando, Fla, USA, (1985). E.N. Chukwu, On boundedness of solutions of third-order diferential equations, Ann. Mat. Pura. Appl., Vol.104, No.4, pp.123-149 (1975).
- V. Kolmanovskii, L. Shaiket, Construction of Lyapunov functionals for stochastic hereditary systems. A survey of some recent results, Mathematical and computer modelling, Vol.36, No.6, pp.691-716 (2002).
- C. Lamberto, Asymptotic behaviour and stability problems in ordinary diferential equations, Springer-Verlag Berlin Heidelberg, (1956).
- R. Liu, Y. Raoul, Boundedness and exponential stability of highly nonlinear stochastic diferential equations, Electronic Journal of Diferential Equations, No.143, pp.1{10 (2009).
- A.M. Mahmoud, C. Tunc, Asymptotic stability of solutions for a kind of thirdorder stochastic diferential equation with delays, Miskole Mathematical Note, Vol.20, No.1, pp.381-393 (2019).
- X. Mao, Some contributions to stochastic asymptotic stability and boundedness via multiple Lyapunov functions, Journal of Mathematical Analysis and Applications, Vol.260, pp.325-340 (2001).
- B. Oksendal, Stochastic Diferential Equations: An introduction with applications, springer, (2000).
- B.S. Ogundare, A.T. Ademola, M.O. Ogundiran, O.A. Adesina, On the qualitative behaviour of solutions to certain second-order nonlinear diferential equation with delay. Annalidell Universita di Ferrara, (2016).
- Y.N. Raoul, Boundedness and exponential asymptotic stability in dynamical systems with applications to nonlinear diferential equations with unbounded terms, Advances in Dynamical Systems and Applications, Vol.2, No.1, pp.107-121 (2007).
- A. Rodkina, M. Basin, On delay-dependent stability for a class of nonlinear stochastic delay-diferential equations, Mathematics of Control, Signals, and Systems, Vol.18, No.2, pp.187{197 (2006).
- L. Shaikihet, Lyapunov functional and stability of stochastic functional diferential equations, Springer, International, (2013).
- T. Yoshizawa, Stability theory by Liapunov's second method, The Mathematical Society of Japan, (1966).
Toplam 27 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Adi Diferansiyel Denklemler, Fark Denklemleri ve Dinamik Sistemler, Temel Matematik (Diğer) |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 15 Ekim 2023 |
| Gönderilme Tarihi | 19 Ağustos 2023 |
| Kabul Tarihi | 14 Ekim 2023 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 6 Sayı: 3-Supplement |
