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Construction of Fundamental Solution for an Odd-Order Equation

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Abstract

In previous papers, we obtained some delta-shaped partial solutions of odd-order equations with multiple characteristics and studied some of their properties. In this paper, we first obtain the necessary estimates at infinity for these solutions, and then construct a fundamental solution (FS) of an odd-order equation with multiple characteristics in a rectangular domain as the sum of these particular solutions. We show that the FS is a solution to an inhomogeneous equation with multiple characteristics in a rectangular domain. In turn, knowledge of FS allows us to construct a potential theory for its further use in solving boundary-value problems.

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Namangan Engineering and Construction Institute, 160103, Namangan, Uzbekistan

    B. Yu. Irgashev

  2. V.I. Romanovskiy Institute of Mathematics, 100174, Tashkent, Uzbekistan

    B. Yu. Irgashev

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  1. B. Yu. Irgashev
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Correspondence to B. Yu. Irgashev.

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Translated by E. Seifina

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Irgashev, B.Y. Construction of Fundamental Solution for an Odd-Order Equation. Vestnik St.Petersb. Univ.Math. 56, 512–520 (2023). https://doi.org/10.1134/S1063454123040180

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  • DOI: https://doi.org/10.1134/S1063454123040180

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