Boundary value problem with asymmetric boundary conditions for a third-order equation with variable coefficients

Abstract

In this paper, a boundary value problem with asymmetric conditions for a third-order inhomogeneous equation with multiple characteristics containing lower-order terms is studied. The uniqueness of the solution to the problem is proved by the energy integral method. It is shown that if the uniqueness theorem condition is violated, the homogeneous problem has a nontrivial solution. The existence of this is proved by the Fourier method. The solution to the stated problem is obtained in an explicit form with the help of the constructed Green function. Uniform convergence of the series and their derivatives included in the equation is proved.

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Identifiers

DOI

10.26907/0021-3446-2026-5-19-30

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