Asymptotic behavior of solutions of Volterra integro-differential equations

Authors:
M. Rama Mohana Rao and P. Srinivas

Journal:
Proc. Amer. Math. Soc. **94** (1985), 55-60

MSC:
Primary 45J05

DOI:
https://doi.org/10.1090/S0002-9939-1985-0781056-5

MathSciNet review:
781056

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Abstract | References | Similar Articles | Additional Information

Abstract: The asymptotic behavior of solutions of Volterra integrodifferential equations of the form

**[1]**T. A. Burton,*Stability theory for Volterra equations*, J. Differential Equations**32**(1979), 101-118. MR**532766 (80f:45016)****[2]**-,*Uniform stability for Volterra equations*, J. Differential Equations**36**(1980), 40-53. MR**571126 (81f:45015)****[3]**-,*An integro-differential equation*, Proc. Amer. Math. Soc.**79**(1980), 393-399. MR**567979 (81h:45018)****[4]**W. A. Coppel,*Stability and asymptotic behavior of differential equations*, Heath, Boston, Mass., 1965. MR**0190463 (32:7875)****[5]**-,*Dichotomies in stability theory*, Lecture Notes in Math., vol. 629, Springer-Verlag, Berlin and New York, 1978. MR**0481196 (58:1332)****[6]**R. Grimmer and G. Seifert,*Stability properties of Volterra integro-differential equations*, J. Differential Equations**19**(1975), 142-166. MR**0388002 (52:8839)****[7]**S. I. Grossman and R. K. Miller,*Nonlinear Volterra integro-differential systems with**-kernels*, J. Differential Equations**13**(1973), 551-566. MR**0348417 (50:915)****[8]**-,*Perturbation theory for Volterra integro-differential systems*, J. Differential Equations**8**(1970), 451-474.**[9]**J. J. Levin,*The asymptotic behavior of the solution of a Volterra equation*, Proc. Amer. Math. Soc.**14**(1963), 534-541. MR**0152852 (27:2824)****[10]**V. Lakshmikantham and M. Rama Mohana Rao,*Integro-differential equations and extension of Liapunov's method*, J. Math. Anal. Appl.**30**(1970), 435-447. MR**0254549 (40:7757)****[11]**R. E. A. C. Paley and N. Wiener,*Fourier transforms in complex domain*, Amer. Math. Soc, Providence, R.I., 1934. MR**1451142 (98a:01023)****[12]**M. Rama Mohana Rao,*Ordinary differential equations--Theory and applications*, Edward Arnold, London, 1981. MR**587850 (82f:34001)****[13]**M. Rama Mohana Rao and Chris P. Tsokos,*Integro-differential equations of Volterra type*, Bull. Austral. Math. Soc.**3**(1970), 9-22. MR**0278027 (43:3759)****[14]**G. Seifert,*Liapunov-Razumikhin conditions for stability and boundedness of functional differential equations of Volterra type*, J. Differential Equations**14**(1973), 424-430. MR**0492745 (58:11816)****[15]**-,*Liapunov-Razumikhin conditions for asymptotic stability in functional differential equations of Volterra type*, J. Differential Equations**16**(1974), 289-298. MR**0460837 (57:829)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0781056-5

Keywords:
Integro-differential equation,
equivalent equation,
arbitrary function,
differential resolvent

Article copyright:
© Copyright 1985
American Mathematical Society