Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients
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.
Fields of Study & Subjects
Differential Equations and Boundary Problems
Nonlinear Differential Equations Analysis
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Ukrains’kyi Matematychnyi Zhurnal
- Volume
- 78
- Issue
- 1-2
- Pages
- 77–78
- Publication date
- 27 January 2026
- Language
- EN