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Functional-Differential Equations with Dilation and Symmetry

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Abstract

We examine the Dirichlet problem in a bounded plane domain for a strongly elliptic functional-differential equation of the second order containing the argument transformations \( x\mapsto px \) (\( p>0 \)) and \( x\mapsto-x \) in higher-order derivatives. The study of solvability of the problem relies on a Gårding-type inequality for which some necessary and sufficient conditions are obtained in algebraic form.

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Funding

The authors were supported by the Ministry for Education and Science of the Russian Federation within the framework of the State Task (Grant no. 075–03–2020–223/3) (FSSF–2020–0018).

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia, Moscow, Russia

    L. E. Rossovskii

  2. Kadyrov Chechen State University, Grozny, Russia

    A. A. Tovsultanov

Authors
  1. L. E. Rossovskii
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  2. A. A. Tovsultanov
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Corresponding author

Correspondence to L. E. Rossovskii.

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 4, pp. 911–923. https://doi.org/10.33048/smzh.2022.63.416

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Rossovskii, L.E., Tovsultanov, A.A. Functional-Differential Equations with Dilation and Symmetry. Sib Math J 63, 758–768 (2022). https://doi.org/10.1134/S0037446622040164

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  • DOI: https://doi.org/10.1134/S0037446622040164

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