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

Authors

  • Yusupjon Apakov V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan; Namangan State Technical University, Namangan, Uzbekistan
  • Raxmatilla Umarov Andijan Institute of Agriculture and Agrotechnologies, Andijan, Uzbekistan

DOI:

https://doi.org/10.3842/umzh.v78i1-2.8975

Keywords:

Differential equation, third order, multiple characteristics, asymmetric boundary value problem, regular solution, uniqueness, existence, Green’s function.

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.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 1-2, 2026.

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Published

26.01.2026

Issue

Vol. 78 No. 1-2 (2026)

Section

Research articles

License

Copyright (c) 2026 Yusupjon Apakov, Raxmatilla Umarov

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Apakov, Yusupjon, and Raxmatilla Umarov. “Solutions of a Time-Asymmetric Boundary-Value Problem for a Third-Order Equation With Variable Coefficients”. Ukrains’kyi Matematychnyi Zhurnal, vol. 78, no. 1-2, Jan. 2026, pp. 77–78, https://doi.org/10.3842/umzh.v78i1-2.8975.