Abstract
We show that a solution of the Dirichlet problem for an elliptic equation of the fourth order with constant coefficients, whose right-hand side is periodic in all variables except one and exponentially decreases, converges at infinity to a certain polynomial of the first degree in the nonperiodic variable. Coefficients of this polynomial are determined.
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References
V. I. Sukretnyi, On the Behavior at Infinity of Solutions of Elliptic Equations of Higher Orders in an Unbounded Domain [in Russian], Preprint No. 88.15, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1988).
O. A. Oleinik and G. A. Iosif’yan, Mathematical Problems of the Theory of Strongly Inhomogeneous Elastic Media [in Russian], Nauka, Moscow (1990).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 3, pp. 437–444, March, 1998.
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Obaid, F.S. On the limit polynomial for a solution of an elliptic equation of the fourth order with constant coefficients. Ukr Math J 50, 498–506 (1998). https://doi.org/10.1007/BF02528816
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DOI: https://doi.org/10.1007/BF02528816