This article is cited in 3 papers

Differentical equations, dynamical systems and optimal control

On a boundary value problem for a high order mixed type equation

B. Yu. Irgashev

Namangan Engineering Construction Institute, Uzbekistan 12, I. Karimov ave., Namangan, 160103, Uzbekistan

Abstract: In this paper, we study a Dirichlet type problem for a Lavrentiev–Bitsadze type equation of high order type in a rectangular domain. The necessary and sufficient conditions for the uniqueness of the problem solution are obtained by using the spectral method. The solution is constructed in the form of a series of eigenfunctions. When substantiating the convergence of a series, the problem of «small» denominators arises. Sufficient conditions are obtained for the separability of the «small» denominator from zero.

Keywords: Differential equation, mixed type, boundary value problem, eigenvalue, eigenfunction, determinant, uniqueness, existence, «small» denominators, series, convergence.

UDC: 517.953

MSC: 35M99

Received December 14, 2019, published July 8, 2020

Language: English

DOI: 10.33048/semi.2020.17.066

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