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<p>We study a problem with Dirichlet–Neumann conditions with respect to time and the conditions of almost periodicity with respect to spatial coordinates for high-order inhomogeneous partial differential equations unsolved with respect to the highest-order time derivative in a multidimensional infinite layer. The conditions required for the unique solvability of this problem are established and its solution is constructed. The analysis of solvability of the investigated problem is connected with the problem of small denominators for which lower estimates are obtained by the metric approach.</p>

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Dirichlet–Neumann Problem for Partial Differential Equations Unsolved With Respect to the Highest Time Derivative

  • 期刊论文

  • 发表日期：

    2026年5月19日

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  • P. Ya. Pukach,
  • S. M. Repetylo

摘要

We study a problem with Dirichlet–Neumann conditions with respect to time and the conditions of almost periodicity with respect to spatial coordinates for high-order inhomogeneous partial differential equations unsolved with respect to the highest-order time derivative in a multidimensional infinite layer. The conditions required for the unique solvability of this problem are established and its solution is constructed. The analysis of solvability of the investigated problem is connected with the problem of small denominators for which lower estimates are obtained by the metric approach.