Article

Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients

Yusupjon ApakovV. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan; Namangan State Technical University, Namangan, UzbekistanRaxmatilla UmarovAndijan Institute of Agriculture and Agrotechnologies, Andijan, Uzbekistan

Ukrains’kyi Matematychnyi Zhurnaljournal2026

ABI

Abstract

UDC 517.951 We study a boundary-value problem with asymmetric time conditions for a third-order inhomogeneous equation with multiple characteristics of lowest-order terms. The unique solvability of the problem is proved by the energy-integral method. It is shown that if the uniqueness condition is violated, then the homogeneous problem has a nontrivial solution. The existence is proved by the Fourier method. The solution of the stated problem is obtained in the explicit form by using the constructed Green's function. The uniform convergence of the solutions and their derivatives contained in the equation is proved.

Topics

Differential Equations and Boundary Problems Stability and Controllability of Differential Equations Nonlinear Differential Equations Analysis

Identifiers

DOI: 10.3842/umzh.v78i1-2.8975

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