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The Journal of Dynamical Systems and Geometric Theories (JDSGT) is a world leading journal publishing high quality, rigorously peer-reviewed original research on dynamical systems and geometry, including the interactions between these two subjects and interdisciplinary research with other branches of knowledge since 2003. Topics published by the Journal include but are not limited to: Random dynamical systems Geometry and physics Dynamical systems with hyperbolic behaviour Real and complex geometry Ergodic theory Distance geometry Topological dynamics Global differential geometry Infinite-dimensional Hamiltonian systems Symplectic geometry, contact geometry The journal considers original research articles, survey articles, and book reviews for publication. Responses to articles and correspondence will also be considered at the Chief Editor’s discretion.

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Open Access Research Article

Some theorems on approximation of solutions of integro-difference-differential equation with nonlocal condition in Banach space

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pp. 127–152Vol. 21Issue 2November 2023DOI: 10.47974/JDSGT-21-2-P10XML
Published Online:
28 Nov 2023
Article type:
Research Article
Language:
EN
Article no.:
JDSGT-21-2-P10
Pages:
127–152

Abstract

Results on approximate solutions, closeness, continuous dependence of solutions of a certain integro- differential equation with finite delay with nonlocal condition in Banach Space are discussed. The integral inequality established by B.G. Pachpatte is used to obtain the results.

Keywords

Subject Classifications

34A1245N0547G2034K0547H10

References

[1] Bielecki A., Une Remarque Sur la method de Banach-Cacciopoli-Tikhnov dans la theorie des equations diffeerentilles ordinaries, Bull. Acad. Polon. Sci. Ser. Sci. Math. Phys. Astr., 4, 261-264(1956).[2] Bellman R. and Cooke K. L., Differential-Difference Equations,Academic Press, New York, (1963).[3] Corduneanu C., Bielecki's Method in the Theory of Integral Equations, Ann.Univ. Mariae Curie-Sklodowska, Section A, 38, 23-40(1984).[4] Corduneanu C., Integral Equations and Applications, Cambridge University Press, (1991).[5] Driver R. D., Ordinary and Delay Differential Equations, Appl. Math. Sci. 20, Springer, New York, (1977).[6] Hale J. K., Theory of Functional Differential Equations, Springer-Verlag, New York, (1977).[7] Kung Y., Delay Differential Equations with Applicationsin Population Dynamics, Academic Press, New York, (1993).[8] Pachpatte B. G., Existence and Uniqueness Theorems on Certain Difference-Differential Equations, Electronic Journal of Diffrential Equations, Vol. 2009, No. 49, 1-12(2009).[9] Pachpatte B. G., Inequalities for Differential and Integral Equations, Academic Press, New York, (1998).[10] Pachpatte B. G., Inegral and Finite Difference Inequalities and Applications, North-Holland Mathematics Studies, Vol.205, Lesevier Science B. V., Amsterdam, (2006).[11] Pachpatte B. G., On a Nonlinear Volterra Integral-Functional Equation, Funkcialaj Ekvacioj, 26, 1-9 (1983).[12] Pachpatte B. G., Some Basic Theorems on Difference-Differential Equations, Electronic Journal of Differential Equations, Vol. 2008, No. 75, 1-11(2008).[13] Pachpatte B. G., Approximation of solutions of a difference-differential equation, Archivum Mathematicum (BRNO), Tomus 46, 145-155(2010).[14] Stokes A., The Applications of a Fixed Point Theorem to a Variety of Non-Linear Stability Problems, Contributions to the Theory of Nonlinear Oscillations, V. Ann. Math. Studies, 45, 173-184(1960).[15] Sugiyama S., Dependence Properties of Solutions of the Retardation and Initial Values in the Theory of Difference-Diffrential Equations, Kodai Math. Sem. Rep.,15, 67-78(1963).[16] Sugiyama S., Existence Theorems on Difference-Differential Equations, Proc. Japan Acad., 38, 145-149(1962).[17] Sugiyama S., On the Boundednes of Solutions of Difference-Differential Equations, Proc. Japan Acad., 36, 456-460(1960).[18] Sugiyama S., On the Existence and Uniqueness Theorems of Difference-Differential Equations,Kodai Math. Sem. Rep.,12, 179-190(1960).[19] Tidke H.L. and More R. T., Existence and Uniqueness of Mild Solutions of Nonlinear Difference-Integrodifferential Equation with Nonlocal Condition, Jounal of Advances in Mathematic, Vol 9,No.3, 1044-1049(2014).[20] Tidke H.L. and More R. T., Existence and uniqueness of mild solutions of nonlinear difference-integrodifferential equation with nonlocal condition, Jounal of Advances in Mathematic, Vol9, No.3, 2415-2430(2014), https://doi.org/10.24297/jam.v9i3.2427 [21] Tidke H.L. and More R. T., Existence and osgood type uniqueness of mild solutions of nonlinear integrodi erential equation with nonlocal condition, International Journal of Pure and Applied Mathematics, Vol.104 No. 3, 437-460(2015), doi:http://dx.doi.org/10.12732/ijpam.v104i3.12[22] Tidke H.L., On the solutions of nonlinear second order differential equation with finite delay, Journal of Advances in Mathematics, Vol. 11, No. 9, 5666-5673(2016).
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