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Approximation of a bounded solution of a linear difference equation on Z2 by solutions of corresponding boundary-value problems in a Banach space

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Abstract

We study the problem of existence and uniqueness of solutions of boundary-value difference problems in a Banach space that correspond to a certain difference equation on Z2. We prove a theorem on approximation of the unique bounded solution of the considered equation by solutions of the corresponding boundary-value problems.

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References

  1. M. F. Gorodnii and A. V. Dorogovtsev, “On stationary solutions of a stochastic two-dimensional difference equation,” in:Stochastic Analysis and Its Applications [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1989), pp. 25–33.

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  2. M. F. Gorodnii, “Bounded and periodic solutions of a difference equation and its stochastic analog in a Banach space,”Ukr. Mat. Zh.,43, No. 1, 41–46 (1991).

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  4. M. F. Gorodnii, “Approximation of a bounded solution of a difference equation by solutions of the corresponding boundary-value problems in a Banach space,”Mat. Zametki,51, No. (4), 17–22 (1992).

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Authors and Affiliations

  1. Kiev University, Kiev

    M. F. Gorodnii

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  1. M. F. Gorodnii
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 535–541, April, 1995.

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Gorodnii, M.F. Approximation of a bounded solution of a linear difference equation on Z2 by solutions of corresponding boundary-value problems in a Banach space. Ukr Math J 47, 622–628 (1995). https://doi.org/10.1007/BF01056049

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  • DOI: https://doi.org/10.1007/BF01056049

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