Hyers-Ulam Stability Of Nonautonomous Third Order Nonlinear Differential Equations
DOI:
https://doi.org/10.60787/tnamp.v21.475Keywords:
Hyers-Ulam stability, Gronwall-Bellman-Bihari type inequality, Integral inequality , Hyers-Ulam constantAbstract
Hyers-Ulam stability of non-autonomous third order nonlinear differential equations is considered in this paper. This consideration is possible by using the Bihari integral inequality and Gronwall-Bellman-Bihari integral inequality to prove Hyers-Ulam stability and determine Hyers-Ulam constant of every non-autonomous third order nonlinear differential equation considered. Our results improve and extend known results in literature.
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Aligaifiary H. Q. and Jung, S -M. : On the Hyers-Ulam Stability of Differential Equations of Second Order. Hindawi Publishing Cooperation Abstract and Appliedd Analysis Volume(2014),1-8.
Alsina C. and Ger R. : On Some Inequalities and Stability Result Related to the Exponential Function. J. Inequl. Appl.2(1988), 373-38
Bihari I. : A generalisation of a Lemma of Bellman and its Application to Uniqueness Problem of Differential Equations. -Acta Maths. Acad. Sc. Hung. 7(1956), 71-94.
Dhongade D.G. and Deo S.G. : Some Generalisations of Bellman-Bihari Integral Inequalities. Journal of Mathematical Analysis and Applications 44(1973,)218-226.
Fakunle I. and Arawomo P.O. : Hyers-Ulam-Rassias stability of a Certain Perturbed Nonlinear Lienard Type Differential Equation. Unilag Journal of Mathematics and Applications,Volume 3, (2023), 1-16.
Fakunle.I and Arawomo P. O. : Hyers-Ulam-Rassias stability of Nonlinear Second Order of A Perturbed Ordinary Differential Equation. Proyecciones Journal of Mathematics. Vol 42,No 5, (2023),1157-1157, 2022.
Fakunle I. and Arawomo, P. O. : Hyers-Ulam Stability of a Perturbed Generalised Lienard Equation. International Journal of Applied Mathematics.32,No.3(2019),479-489.
Fakunle I. and Arawomo.P.O. : Hyers-Ulam Stability of Certain Class of Nonlinear Second Order Differential Equations. International Journal of Pure and Applied Mathematical Sciences.11(1)(2018),55-65.
Fakunle I. and Arawomo,P.O. : On Hyers-Ulam Stability of Nonlinear Second Order Ordinary and Functional Differential Equations. International Journal of Differential Equations and Applications 17(1)(2018)77-88.
Gavruta P. Jung S-M. Li Y. : Hyers-Ulam Stability for Second Order Liner Differential Equations with Boundary Conditions.EJDE 80(2011) pp1-7.
Ince E.L. : Ordinary differential Equation. Messer.Longmans,Green and co. Heliopolis,pp42,(1926).
Jung S-M. Hyers-Ulam Stability of Linear Differential Equations of First Order. Appl.Math.Lett.17(2004),1135-1140.
Jung S-M. : : Hyers-Ulam Stability of Linear Differential Equations of First Order. Journal of Mathematics Analysis and Applications 33(2005)139-146.
Jung S-M. : Hyers-Ulam Stability of Linear Differential Equations of First Order(II) Appl.Math.Lett.19(2006)854-858.
Li Y. : Hyers-Ulam Stability of Linear Differential Equations of First Order. Thai Journal of Mathematics 8(2) (2010)215-219.
Li Y., Shen Y. : Hyers-Ulam Stability of Nonhomogenous Linear Differential Equations of Second Order International Journal of Mathematics and Mathematical Sciences (2009), Article ID576852, pp7.
Obloza M. : Hyers-Ulam Stability of the Linear Differential Equations. Rocznik Nauk. Dydakt-Dydakt. Prac. Mat.13(1993), 259-270.
Murray R. S.: Schum’s Outline of Theory and Problem of Calculus, SI(Metric) Edition , International Edition 1974.
Murali R. and Ponmana Selvan A. Hyers-Ulam Stability of Third Order Linear Differential Equation. Journal of Computer Mathematical Science.9(10)(2018),1334-1340.
Murali R. and Ponmana Selvan A. : Hyers-Ulam-Rassias Stability for the Linear Ordinary Differential Equation of Third Order. Kragujevac Journal of Mathematics 42(4) (2018),579-590.
Miura T. ,Jung,S.-M. Takahasi,S.E. : Hyers -Ulam-Rassias Stability of the Banach Space Valued Linear Differential Equations
y'=λy
y
′
=
????
y
Korean Mathematics Society41(2004)99-1005.
Qarawani M. N. : Hyers-Ulam Stability of Linear and Nonlinear Differential Equations of Second Order. Int. Journal of Applied Mathematical Research1(4)(2012), 422-432.
Qarawani M. N.: Hyers-Ulam Stability of a Generalised Second Order Nonlinear Differential Equations. Applied Mathematics, 3(2012)1857-1861.
Rassias T. M.: On the Stability of the Linear Mapping in Banach Spaces. Proceedings of the American Mathematical Society, 72(2)(1978),297-300
Rus I.A. : Ulam Stability of Ordinary Differential Equation Studia Universities Babes-Bolyal Mathematical, 54(4)(2010),306-309.
Rus I. A. : Ulam stability of Ordinary Differential Equations in a Banach Space. Carpathian, J.Math.26(1)(2010)103-107.
Tripathy A.K. and Satapathy A.: Hyers-Ulam Stability of Third Order Euler’s Differential Equations Journal of Nonlinear Dynamics.(2014),Article I.D 4872577,6 pages
Wang G., Zhou M. and L.Sun Hyers-Ulam Stability of Linear Differential Equations of First Order Appl.Math.Lett 21(2008),1024-1028.
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