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On the Solution of Some Non-Local Problems

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Abstract

This paper deals with two types of non-local problems for the Poisson equation in the disc. The first of them deals with the situation when the function value on the circle is given as a combination of unknown function values in the disc. The other type deals with the situation when a combination of the value of the function and its derivative by radius on the circle are given as a combination of unknown function values in the disc. The existence and uniqueness of the classical solution of these problems is proved. The solutions are constructed in an explicit form.

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Authors and Affiliations

  1. Department of Mathematics, Málaga University, Spain

    F. Criado

  2. Department of Applied Physics, Málaga University, Spain

    F. Criado Jr.

  3. Department of Applied Mathematics and Computer Science, Tbilisi State University, Georgia, USA

    N. Odishelidze

Authors
  1. F. Criado
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  2. F. Criado Jr.
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  3. N. Odishelidze
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Criado, F., Criado, F. & Odishelidze, N. On the Solution of Some Non-Local Problems. Czechoslovak Mathematical Journal 54, 487–498 (2004). https://doi.org/10.1023/B:CMAJ.0000042586.11198.79

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  • DOI: https://doi.org/10.1023/B:CMAJ.0000042586.11198.79

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