An remainder theorem for an integrodifferential equation with asymptotically periodic solution
Author:
Kenneth B. Hannsgen
Journal:
Proc. Amer. Math. Soc. 73 (1979), 331337
MSC:
Primary 45D05; Secondary 45J05, 45M05
MathSciNet review:
518514
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Abstract: For a certain integrodifferential equation of Volterra type on , with piecewise linear convolution kernel, it is shown that the solution is , with and and constant; is represented similarly.
 [1]
R. W. Carr and K. B. Hannsgen, A nonhomogeneous integrodifferential equation in Hilbert space, SIAM J. Math. Anal. (to appear).
 [2]
S.
I. Grossman and R.
K. Miller, Nonlinear Volterra integrodifferential systems with
𝐿¹kernels, J. Differential Equations 13
(1973), 551–566. MR 0348417
(50 #915)
 [3]
Kenneth
B. Hannsgen, Indirect abelian theorems and a linear
Volterra equation, Trans. Amer. Math. Soc.
142 (1969),
539–555. MR 0246058
(39 #7364), http://dx.doi.org/10.1090/S00029947196902460581
 [4]
Kenneth
B. Hannsgen, Uniform boundedness in a class of Volterra
equations, SIAM J. Math. Anal. 6 (1975),
689–697. MR 0370107
(51 #6336)
 [5]
G.
S. Jordan and Robert
L. Wheeler, On the asymptotic behavior of perturbed Volterra
integral equations, SIAM J. Math. Anal. 5 (1974),
273–277. MR 0342976
(49 #7720)
 [6]
R.
K. Miller, Structure of solutions of unstable linear Volterra
integrodifferential equations, J. Differential Equations
15 (1974), 129–157. MR 0350351
(50 #2844)
 [7]
Daniel
F. Shea and Stephen
Wainger, Variants of the WienerLévy theorem, with
applications to stability problems for some Volterra integral
equations, Amer. J. Math. 97 (1975), 312–343.
MR
0372521 (51 #8728)
 [1]
 R. W. Carr and K. B. Hannsgen, A nonhomogeneous integrodifferential equation in Hilbert space, SIAM J. Math. Anal. (to appear).
 [2]
 S. I. Grossman and R. K. Miller, Nonlinear Volterra integrodifferential systems with kernels, J. Differential Equations 13 (1973), 551566. MR 0348417 (50:915)
 [3]
 K. B. Hannsgen, Indirect abelian theorems and a linear Volterra equation, Trans. Amer. Math. Soc. 142 (1969), 539555. MR 0246058 (39:7364)
 [4]
 , Uniform boundedness in a class of Volterra equations, SIAM J. Math. Anal. 6 (1975), 689697. MR 0370107 (51:6336)
 [5]
 G. S. Jordan and R. L. Wheeler, Structure of resolvents of Volterra integral and integrodifferential systems (to appear). MR 0342976 (49:7720)
 [6]
 R. K. Miller, Structure of solutions of unstable linear Volterra integrodifferential equations, J. Differential Equations 15 (1974), 129157. MR 0350351 (50:2844)
 [7]
 D. F. Shea and S. Wainger, Variants of the WienerLévy theorem, with applications to stability problems for some Volterra integral equations, Amer. J. Math. 97 (1975), 312343. MR 0372521 (51:8728)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197905185141
PII:
S 00029939(1979)05185141
Article copyright:
© Copyright 1979
American Mathematical Society
