Abstract
In this research we utilize Lyapunov functionals to obtain boundedness on all solutions, exponential stability and \(l_p\)-stability on the zero solution of summation equations and Volterra difference equations.
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References
Adivar, M., Raffoul, Y.: Existence of Resolvent for Volterra integral equations on time scales. Bull. Aust. Math. Soc. 82, 139–155 (2010)
Adivar, M., Raffoul, Y.: Qualitative analysis of nonlinear Volterra integral equations on time scales using and Lyapunov functionals. Appl. Math. Comput. 273, 258–266 (2016)
Bohner, M., Peterson, A.: Dynamic Equations on Time Scales. An Introduction with Applications. Birkhäuser, Boston (2001)
Elaydi, S.: An Introduction to Difference Equations, 3rd edn. Springer, New York (2005)
Kelley, W., Peterson, A.: Difference Equations An Introduction With Applications, 2nd edn. Academic Press, New York (2001)
Lakshmikantham, L., Trigiante, D.: Theory of Difference Equations: Numerical Methods and Applications. Academic Press, New York (1991)
Medina, R.: Solvability of discrete Volterra equations in weighted spaces. Dyn. Syst. Appl. 5, 407–422 (1996)
Messina, E., Vecchio, A.: Stability analysis of linear Volterras equations on time scales under bounded perturbations. Appl. Math. Lett. 59, 6–11 (2016)
Raffoul, Y.N.: Qualitative Theory of Volterra Difference Equations. Springer, Ney York (2018)
Raffoul, Y.N.: Qualitative analysis of nonconvolution Volterra summation equations. Int. J. Differ. Equ. 14(1), 75–89 (2019)
Zhang, S.: Stability of neutral delay difference systems. Comput. Math. Appl. 42, 291–299 (2001)
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Raffoul, Y. (2020). Recent Results on Summations and Volterra Difference Equations via Lyapunov Functionals. In: Baigent, S., Bohner, M., Elaydi, S. (eds) Progress on Difference Equations and Discrete Dynamical Systems. ICDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 341. Springer, Cham. https://doi.org/10.1007/978-3-030-60107-2_18
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DOI: https://doi.org/10.1007/978-3-030-60107-2_18
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