Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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ULAM STABILITIES FOR IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS

  • Sandhyatai D. Kadam (Department of Mathematics, Dr. D. Y. Patil Institute of Technology) ;
  • Radhika Menon (Department of Mathematics, Dr. D. Y. Patil Institute of Technology) ;
  • R. S. Jain (Department of Mathematics, Swami Ramanand Teerth Marathwada University) ;
  • B. Surendranath Reddy (Department of Mathematics, Swami Ramanand Teerth Marathwada University)
  • Received : 2023.07.14
  • Accepted : 2023.09.10
  • Published : 2024.03.15
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Abstract

In the present paper, we establish Ulam-Hyres and Ulam-Hyers-Rassias stabilities for nonlinear impulsive integro-differential equations with non-local condition in Banach space. The generalization of Grownwall type inequality is used to obtain our results.

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References

  1. M Asadi, Exact Solutions of Singular IVPs Lane-Emden Equation, Comm. Nonlinear Anal., 6(1) (2019), 60-63.
  2. D. Bainov and Snezhana G. Haristova , Integral Inequalities of Gronwall type for piecewise continuous functions, J. Appl. Math. Stoc. Anal., 10(1) (1997), 89-94. https://doi.org/10.1155/S1048953397000099
  3. D. Bainov and Pavel Simeonov, Impusive Differential Equations, Periodic Solutions and Applications, 1993.
  4. M. Benchora, J. Henderson and S.K. Ntouyas, An existence Result for first order impulsive functional differential equations in Banach spaces, Comput. Math. Appl., 42 (2001), 1303-1310. https://doi.org/10.1016/S0898-1221(01)00241-3
  5. M. Gabeleh, M. Asadi and P.R. Patle, Simulation functions and MeirKeeler condensing operators with application to integral equations, Asian-Europ. J. Math., 15(9) (2022), Artical No. 2250171.
  6. S. Ghezellou, M. Azhini and M. Asadi, New theorems by minimax inequalities on Hspace, Bull. Math. Anal. Appl., 12(2) (2020), 27-34.
  7. D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci., 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  8. Rupali S. Jain and M.B. Dhakne, On impulsive nonlocal integro-differential equations with finite delay, Int. J. of Mathematics Research, 5(4) (2013), 361-373.
  9. Rupali S. Jain and M.B. Dhakne, On Global Existence of solutions for abstract nonlinear functional Integro-Differentai Equations With Nonlocal Condition, Contemporary Mathematics and Statistics, 2023(1) (2013), 44-53.
  10. Rupali S. Jain and M.B. Dhakne, On mild solutions of nonlocal semilinear functional integro-differential equations, Malaya Journal of Matematik, 3(1) (2013), 27-33. https://doi.org/10.26637/mjm103/005
  11. S.D. Kadam, R.S. Jain and B. Surendranath Reddy, On the global existence of mild solutions of impulsive integro-differential equations with nonlocal condition, Open J. of Applied and theoretical mathematics, 2(4) (2016), 1027-1040.
  12. K.D. Kucche and P.U. Shikhare, Ulam stabilities via pachpatte's inequality for Volterra-Fredholm delay integrodifferential equations in Banach spaces, Note di Matematica, Note Mat., 38(1) (2018), 67-82.
  13. G.E. Ladas and V. Lakshmikantham, Differential equations in abstract space, Acsdemic press, 1972.
  14. Xuezhu Li and Jinrong Wang, Ulam-Hyers-Rassias stability of semilinear differential equations with impulses, Electronic Journal of Differential Equations, 2013(172) (2013), 1-8.
  15. Zeng Lin, WeiWei and JinRong Wang, Existence and stability results for impulsive integro-differential equations, FACTA UNIVERSITATIS (NIS) Ser. Math. Inform., 29(2) (2014), 119-130.
  16. V. Lkashmikanthamm, D.D. Bainov and P.S. Simeonov, Theory of impulsive differential equations, World scientific Singapore, 1889.
  17. B.G. Pachpatte, Integral and finite difference inequalities and applications, Northholland Mathematics Studies, 205, Elsevier Science, B.V., Amsterdam, 2006.
  18. C. Parthasarathy, Existence and Hyers-Ulam Stability of nonlinear impulsive differential equations with nonlocal conditions, Electronic Journal of Mathematical Analysis and Applications, 4(1) (2016), 106-115. https://doi.org/10.21608/ejmaa.2016.310817
  19. Th.M. Rassias, On the stability of linear mappings in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
  20. S.M. Ulam, A collection of mathematical problems, Interscience Publishers, New York, 1968.
  21. JinRong Wang, Michal Feckan and Yong Zhou, On the stability of first order impulsive evolution equations, Opuscula Math., 34(3) (2014), 639-657. https://doi.org/10.7494/OpMath.2014.34.3.639
  22. JinRong Wanga, Michal Feckan and Yong Zhou, Ulams type stability of impulsive ordinary differential equations, J. Math. Anal. Appl., 395 (2012), 258-264. https://doi.org/10.1016/j.jmaa.2012.05.040
  23. Akbar Zada, Shah Faisal and Yongjin Li, On the Hyers-Ulam stability of first-order impulsive delay differential equations, Hindawi Publishing Corporation Journal of Function Spaces, Volume 2016, 6 pages, http://dx.doi.org/10.1155/2016/8164978.