Boundedness properties in Volterra integro-differential systems
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- by W. E. Mahfoud PDF
- Proc. Amer. Math. Soc. 100 (1987), 37-45 Request permission
Abstract:
Sufficient conditions are given to insure that all solutions of the integrodifferential system \[ xโ = A(t)x + \int _0^t {C(t,s)x(s)ds + f(t)} \] are uniform bounded.References
- T. A. Burton, Perturbed Volterra equations, J. Differential Equations 43 (1982), no.ย 2, 168โ183. MR 647061, DOI 10.1016/0022-0396(82)90089-4
- T. A. Burton, Periodicity and limiting equations in Volterra systems, Boll. Un. Mat. Ital. C (6) 4 (1985), no.ย 1, 31โ39. MR 805203
- Ronald Grimmer and George Seifert, Stability properties of Volterra integrodifferential equations, J. Differential Equations 19 (1975), no.ย 1, 142โ166. MR 388002, DOI 10.1016/0022-0396(75)90025-X
- S. I. Grossman and R. K. Miller, Nonlinear Volterra integrodifferential systems with $L^{1}$-kernels, J. Differential Equations 13 (1973), 551โ566. MR 348417, DOI 10.1016/0022-0396(73)90011-9
- Jack K. Hale, Ordinary differential equations, Pure and Applied Mathematics, Vol. XXI, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. MR 0419901
- R. K. Miller, Asymptotic stability properties of linear Volterra integrodifferential equations, J. Differential Equations 10 (1971), 485โ506. MR 290058, DOI 10.1016/0022-0396(71)90008-8
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 37-45
- MSC: Primary 45D05; Secondary 34K20, 45J05
- DOI: https://doi.org/10.1090/S0002-9939-1987-0883398-3
- MathSciNet review: 883398