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An $ L\sp{1}$ remainder theorem for an integrodifferential equation with asymptotically periodic solution

Author: Kenneth B. Hannsgen
Journal: Proc. Amer. Math. Soc. 73 (1979), 331-337
MSC: Primary 45D05; Secondary 45J05, 45M05
MathSciNet review: 518514
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Abstract: For a certain integrodifferential equation of Volterra type on $ (0,\infty )$, with piecewise linear convolution kernel, it is shown that the solution is $ u(t) = \alpha \;\cos \beta t + \rho (t)$, with $ \rho \in {L^1}(0,\infty )$ and $ \alpha $ and $ \beta $ constant; $ u'$ is represented similarly.

References [Enhancements On Off] (What's this?)

  • [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 $ {L^1}$-kernels, J. Differential Equations 13 (1973), 551-566. MR 0348417 (50:915)
  • [3] K. B. Hannsgen, Indirect abelian theorems and a linear Volterra equation, Trans. Amer. Math. Soc. 142 (1969), 539-555. MR 0246058 (39:7364)
  • [4] -, 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 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), 129-157. MR 0350351 (50:2844)
  • [7] D. F. Shea and S. Wainger, Variants of the Wiener-Lévy theorem, with applications to stability problems for some Volterra integral equations, Amer. J. Math. 97 (1975), 312-343. MR 0372521 (51:8728)

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