Existence of the solutions to convolution equations with distributional kernels

  • Authors

    • Alexander G. Ramm Mathematics Department, Kansas State University, CW 207, Manhattan, KS 66506-2602, USA

    Received date: November 9, 2017

    Accepted date: December 11, 2017

    Published date: December 14, 2017

    https://doi.org/10.14419/gjma.v6i1.8632
  • Volterra equations, distributional kernels

  • Abstract

    It is proved that a class of convolution integral equations of the Volterra type has a globalsolution, that is, solutions defined for all \(t\ge 0\). Smoothness of the solution is studied.

  • References

    1. [1] I.Gelfand, G. Shilov, Generalized functions, Vol.1, AMS Chelsea Publ., 1964.
      [2] P. Zabreiko, A.Koshelev, M. Krasnoselskii, S.Mikhlin, L. Rakovshchik, V Stecenko, Integral equations: a reference text, Leyden, Noordhoff International Publ., 1975.

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  • How to Cite

    Ramm, A. G. (2017). Existence of the solutions to convolution equations with distributional kernels. Global Journal of Mathematical Analysis, 6(1), 1-1. https://doi.org/10.14419/gjma.v6i1.8632

    Received date: November 9, 2017

    Accepted date: December 11, 2017

    Published date: December 14, 2017