Differential Equations and Mathematical Physics

Nonlocal Tricomi boundary value problem for a mixed-type differential-difference equation

A. N. Zarubin

Orel State University after I. S. Turgenev, Orel, 302026, Russian Federation

Abstract: We investigate the Tricomi boundary value problem for a differential-difference leading-lagging equation of mixed type with non-Carleman deviations in all arguments of the required function. A reduction is applied to a mixed-type equation without deviations. Symmetric pairwise commutative matrices of the coefficients of the equation are used. The theorems of uniqueness and existence are proved. The problem is unambiguously solvable.

Keywords: mixed-type equation, differential-difference equation, integral equation, singular integral equation, concentrated lag and lead.

UDC: 517.956.6

MSC: 35M12

Received: November 5, 2020
Revised: February 13, 2021
Accepted: February 22, 2021
First online: March 10, 2021

DOI: 10.14498/vsgtu1835

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