UDC 517.95

I.M. Aleksandrovych
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
 ialexandrovich@ukr.net

M.V.-S. Sydorov
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
 myksyd@knu.ua

N.I. Lyashko
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine,  lyashko.natali@gmail.com

O.S. Bondar
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine,  alenkajob@gmail.com

ROBEN PROBLEM FOR THE AXISYMMETRIC FOURTH-ORDER HELMHOLTZ EQUATION

REFERENCES

• 1. Lyashko S.I., Sydorov M.V.-S., Lyashko N.I., Alexandrovich I.M. Differential operators defining solutions to iterated hyperbolic-type equations. Cybernetics and Systems Analysis. 2024. Vol. 60, N 5. P. 753–758. https://doi.org/10.1007/s10559-024-00712-4.
• 2. Alexandrovich I.M., Bondar O.S., Lyashko S.I., Lyashko N. I., Sydorov M.V.-S. Integral operators that determine the solution of an iterated hyperbolic-type equation. Cybernetics and Systems Analysis. 2020. Vol. 56. P. 401–409. https://doi.org/10.1007/s10559-020-00256-3.
• 3. Boichuk O.A., Makarov V.L., Feruk V.A. A criterion of solvability of resonant equations and construction of their solutions. Ukrainian Mathematical Journal. 2019. Vol. 71, N 10. P. 1321–1330. URL: https://jnas.nbuv.gov.ua/article/UJRN-0001044008.
• 4. Veselovska O.V., Dostoina V.V., Drohomyretska K.T. Construction of solutions of the Helmholtz equation in a cylindrical coordinate system in the form of homogeneous polynomials in two biorthogonal systems of functions. J. Math. Sci., 2024. Vol. 279, N 2. P. 170–180. https://doi.org/10.1007/s10958-024-07003-5.
• 5. Serkh K., Rokhlin V. On the solution of the Helmholtz equation on regions with corners. Proc. Natl. Acad. Sci. 2016. Vol. 113, P. 9171–9176.
• 6. Gotlib V.Y. Solutions of the helmholtz equation, concentrated near a plane periodic boundary. J. Math Sci. 2000. Vol. 102. P. 4188–4194. https://doi.org/10.1007/BF02673850.
• 7. Alexandrovich I.M., Lyashko S.I., Sydorov M.V.-S. Lyashko N.I., Bondar O.S. Riemann integral operator for stationary and non-stationary processes. Cybernetics and Systems Analysis. 2021. Vol. 57. P. 918–926. https://doi.org/10.1007/s10559-021-00418-x.