Vestnik КRAUNC. Fiz.-Mat. nauki. 2022. vol. 38. no. 1. P. 28-39. ISSN 2079-6641

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MSC 35G30, 35Q53

Research Article

On a boundary value problem for an odd-order equation with multiple characteristics

O. T. Kurbanov

Tashkent State Economic University, Uzbekistan, 100003, Tashkent, Chilanzar district, Ave. Islam Karimov, 49


A nonlinear boundary value problem for a third-order nonlinear equation with multiple characteristics is studied in the article in a curvilinear domain. The unique solvability of the problem is proved. The uniqueness of the solution to the boundary value problem is proved by the energy integral method using some elementary inequalities. An auxiliary problem is considered for the existence of a solution, for which the Green function is constructed. By solving an auxiliary problem, the original problem is reduced to a system of Hammerstein integral equations. The solvability of a nonlinear system is proved by the contracting mapping method.

Key words: nonlinearity, uniqueness, existence, system of Hammerstein equations.

DOI: 10.26117/2079-6641-2022-38-1-28-39

Original article submitted: 09.02.2022

Revision submitted: 16.03.2022

For citation. Курбанов О.Т. On a boundary value problem for an odd order equation with multiple characteristics. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 38: 1, 28-39. DOI: 10.26117/2079-6641-2022-38-1-28-39

The content is published under the terms of the Creative Commons Attribution 4.0 International License (

© Kurbanov O. T., 2022

Competing interests. The author declares that there are no conflicts of interest with respect to authorship and publication.

Contribution and responsibility. The author contributed to the writing of the article and is solely responsible for submitting the final version of the article to the press. The final version of the manuscript was approved by the author.


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Kurbanov Odilzhan Tukhtamuradovich – PhD (Phys. & Math.), Associate Professor, Associate Professor, Dept. Apl. Math., Tashkent State University of Economics, Tashkent, Uzbekistan, ORCID 0000-0003-1360-325x.

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