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.
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