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Boundary-value problem in an infinite layer

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Abstract

We establish necessary and sufficient conditions for a nonlocal two-point boundary-value problem in an infinite layer for the equation

$$\frac{{\partial ^2 u(x,t)}}{{\partial t^2 }} + P\left( {\frac{\partial }{{\partial x}}} \right)\frac{{\partial u(x + h_1 ,t)}}{{\partial t}} + Q\left( {\frac{\partial }{{\partial x}}} \right)u(x + h_2 ,t) = 0,$$

whereP(s) andQ(s) are polynomials ins∈ℂm with constant coefficients, to have infinite type and be degenerate.

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References

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Authors and Affiliations

  1. Khar'kov University, Khar'kov

    I. I. Antypko

  2. Khar'kov Road Transport Institute, Khar'kov

    N. O. Semenova

Authors
  1. I. I. Antypko
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  2. N. O. Semenova
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Translated from Ukrainskii Matematicheskii Zhumal, Vol. 47, No. 3, pp. 400–402, March, 1995.

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Antypko, I.I., Semenova, N.O. Boundary-value problem in an infinite layer. Ukr Math J 47, 465–468 (1995). https://doi.org/10.1007/BF01056308

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  • DOI: https://doi.org/10.1007/BF01056308

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