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

DOI:

https://doi.org/10.14419/gjma.v6i1.8632

Keywords:

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] 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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Published

14-12-2017

Issue

Vol. 6 No. 1 (2018)

Section

Articles

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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