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Volume 13
Issue 10
10.3390/math13101630
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Article

On the Solution of the Navier Problem for the 3-Harmonic Equation in the Unit Ball

by
Valery Karachik
Department of Mathematical Analysis and Methods of Teaching Mathematics, South Ural State University, 454080 Chelyabinsk, Russia
Mathematics 2025, 13(10), 1630; https://doi.org/10.3390/math13101630
Submission received: 12 April 2025 / Revised: 8 May 2025 / Accepted: 14 May 2025 / Published: 15 May 2025
(This article belongs to the Section C1: Difference and Differential Equations)
Versions Notes

Abstract

In this paper, based on a new representation of the Green’s function of the Navier problem for the 3-harmonic equation in the unit ball, an integral representation of the solution of the corresponding Navier problem is found. Then, for the Navier problem for a homogeneous 3-harmonic equation, the obtained representation of the solution is reduced to a form that does not explicitly contain the Green’s function.
Keywords: 3-harmonic equation; biharmonic equation; Navier problem; Green’s function 3-harmonic equation; biharmonic equation; Navier problem; Green’s function

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MDPI and ACS Style

Karachik, V. On the Solution of the Navier Problem for the 3-Harmonic Equation in the Unit Ball. Mathematics 2025, 13, 1630. https://doi.org/10.3390/math13101630

AMA Style

Karachik V. On the Solution of the Navier Problem for the 3-Harmonic Equation in the Unit Ball. Mathematics. 2025; 13(10):1630. https://doi.org/10.3390/math13101630

Chicago/Turabian Style

Karachik, Valery. 2025. "On the Solution of the Navier Problem for the 3-Harmonic Equation in the Unit Ball" Mathematics 13, no. 10: 1630. https://doi.org/10.3390/math13101630

APA Style

Karachik, V. (2025). On the Solution of the Navier Problem for the 3-Harmonic Equation in the Unit Ball. Mathematics, 13(10), 1630. https://doi.org/10.3390/math13101630

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