Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



An abstract linear Volterra equation with a nonconvolution kernel

Author: T. Kiffe
Journal: Proc. Amer. Math. Soc. 82 (1981), 51-57
MSC: Primary 45N05; Secondary 45D05
MathSciNet review: 603600
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the existence and uniqueness of solutions to the equation $ x(t) + \int_0^t {a(t,\tau )Ax(\tau )d\tau = f(t)} $ where $ A$ is an unbounded, positive, selfadjoint operator on a Hilbert space. A representation is given for the solution of this equation.

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

  • [1] Ph. Clément and J. A. Nohel, Abstract linear and nonlinear Volterra equations preserving positivity, SIAM J. Math. Anal. 10 (1979), 365-388. MR 523852 (80b:47095)
  • [2] A. Friedman and N. Shinbrot, Volterra integral equations in Banach space, Trans. Amer. Math. Soc. 126 (1967), 131-179. MR 0206754 (34:6571)
  • [3] G. Gripenberg, On positive, nonincreasing resolvents of Volterra equations, J. Differential Equations 30 (1978), 380-390. MR 521860 (81d:45014)
  • [4] -, On Volterra equations with nonconvolution kernels, Report HTKK-MAT-A118, Helsinki Univ. Technology, 1978.
  • [5] -, On a linear Volterra equations in a Hilbert space, Report HTKK-MAT-A127, Helsinki Univ. Technology, 1978.
  • [6] K. Hannsgen, The resolvent kernel of an integro-differential equation in Hilbert space, SIAM J. Math. Anal. 7 (1976), 481-490. MR 0417861 (54:5909)
  • [7] T. Kiffe and M. Stecher, Properties and applications of the resolvent operator to a Volterra integral equation in Hilbert space, SIAM J. Math. Anal. 11 (1980), 82-91. MR 556498 (81h:45029)
  • [8] J. J. Levin, Remarks on a Volterra equation, delay and functional differential equations and their applications, Academic Press, New York, 1972, pp. 233-255. MR 0402437 (53:6257)
  • [9] R. K. Miller, Nonlinear Volterra integral equations, Benjamin, Menlo Park, California, 1971. MR 0511193 (58:23394)
  • [10] K. Yosida, Functional analysis, Springer-Verlag, Berlin and New York, 1974. MR 0350358 (50:2851)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 45N05, 45D05

Retrieve articles in all journals with MSC: 45N05, 45D05

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society