Inequalities and exponential stability and instability in finite delay Volterra integro-differential equations

被引：8
作者：
Murat Adıvar
Youssef N. Raffoul
机构：
[1] Department of Mathematics, Izmir University of Economics
[2] Department of Mathematics, University of Dayton, Dayton, OH
来源：
Rendiconti del Circolo Matematico di Palermo | 2012年 / 61卷 / 3期
关键词：
Exponential stability; Instability; Liapunov functional; Volterra integro-differential equation;
D O I：
10.1007/s12215-012-0092-4
中图分类号：
学科分类号：
摘要：
We use Liapunov functionals to obtain sufficient conditions that ensure exponential stability of the nonlinear Volterra integro-differential equation, where the constant τ is positive, the function p does not need to obey any sign condition and the kernel q is continuous. Our results improve the results obtained in literature even in the autonomous case. In addition, we give a new criteria for instability. © 2012 Springer-Verlag.
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页码：321 / 330
页数：9
相关论文
共 9 条
  • [1] Adivar M., Raffoul Y.N., Inequalities and exponential decay in time varying delay differential equations, Math. Comput. Model., (2012)
  • [2] Hale J., Theory of Functional Differential Equations, (1977)
  • [3] Hatvani L., Annulus argument in the stability theory for functional differential equations, Differ. Integr. Equ., 10, pp. 975-984, (1997)
  • [4] Knyazhishche L., Scheglov V., On the sign of definiteness of Liapunov functionals and stability of a linear delay equation, Electron. J. Qual. Theory Differ. Equ., 8, pp. 1-13, (1998)
  • [5] Funakubo M., Hara T., Sakata S., On the uniform asymptotic stability for a linear integro-differential equation of Volterra type, J. Math. Anal. Appl., 324, pp. 1036-1049, (2006)
  • [6] Raffoul Y.N., Uniform asymptotic stability in linear Volterra systems with nonlinear perturbation, Int. J. Differ. Equ. Appl., 6, pp. 19-28, (2002)
  • [7] Li Y., Periodic solution of a neutral delay equation, J. Math. Anal. Appl., 214, pp. 11-21, (1997)
  • [8] Vanualailai J., Some stability and boundedness criteria for a class of Volterra integro-differential systems, Electron. J. Qual. Theory Differ. Equ., 12, pp. 1-20, (2002)
  • [9] Wang T., Inequalities and stability for a linear scalar functional differential equation, J. Math. Anal. Appl., 298, pp. 33-44, (2004)
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