STABILITY OF VOLTERA EQUATION ON TIME SCALES

Authors

  • Khong Chi Nguyen nguyenkc69@gmail.com
  • Nguyen Thu Ha Electric Power University

DOI:

https://doi.org/10.51453/2354-1431/2021/627

Abstract

In this paper, we develop a robust stability theorem for Volterra equations on time scales. We prove that these equations are preserved the boundedness and exponential stability under perturbations. The findings can be considered as a generalization for the robust stability of differential and difference Volterra equations.

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References

[1] M. Bohner and A. Peterson (2001), Dynamic equations on time scales: An Introduction with Applications, Birkh¨auser, Boston.

[2] Gusein Sh. Guseinov (2003), Integration on time scales, J. Math. Anal. Appl., 285, 107{127.

[3] L. Yu, Daleckii, M. G. Krein (1971), Stability of Solutions of Differential Equations in Banach Space, Amer. Math. Soc., Providence, RI.

[4] E. Bravyi, R. Hakl, A. Lomtatidze (2002), On Cauchy problem for first order nonlinear functional differential equations of non-Volterra’s type. (English), Czechoslovak Mathematical Journal, 52, issue 4, pp. 673{690.

[5] T.A. Burton (1983), Volterra Equations with Small Kernels, J. Integral Equations, 5, pp. 271{285.

[6] N. H. Du (2008), Stability radii of differential-algebraic equations with structured perturbations, Systems & Control Lett., 57, pp. 546-553.

[7] N.H. Du, V.H. Linh and N.T.T. Nga (2016), On stability and Bohl exponent of linear singular systems of difference equations with variable coefficients, J. Differ. Equ. Appl., 22, pp. 1350{1377.

[8] N.H. Du, L.H. Tien (2007), On the exponential stability of dynamic equations on time scales. J. Math. Anal. Appl., 331, pp. 1159{1174.

[9] Sung Kyu Choi and Namjip Koo (2010), On a Gronwall-type inequality on time scales. Journal of

Chungcheong maththematica society, 23(1).

[10] R. Grimmer and G. Seifert (1975), Stability Properties of Integrodifferential Equations, J. Differential Equations, 19, pp. 142{166.

[11] S. Grossman and R.K. Miller (1970), Perturbation Theory for Volterra Integrodiffererential Systems, J. Differential Equations, 8, pp. 457{474.

[12] M. Pituk (2004), A criterion for the exponential stability of linear difference equations, Appl. Math. Lett., 17 , pp. 779{783.

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Published

2022-04-12

How to Cite

Khổng, C. N., & Nguyễn Thu, H. (2022). STABILITY OF VOLTERA EQUATION ON TIME SCALES. SCIENTIFIC JOURNAL OF TAN TRAO UNIVERSITY, 7(24). https://doi.org/10.51453/2354-1431/2021/627

Issue

Vol. 7 No. 24 (2021): No. 24, DECEMBER-2021

Section

Natural Science and Technology

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