Boundary-Value Problems for Differential-Difference Equations with Incommeasurable Shifts of Arguments Reducible to Nonlocal Problems

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Abstract


We consider boundary-value problems for differential-difference equations containing incommeasurable shifts of arguments in higher-order terms. We prove that in the case of finite orbits of boundary points generated by the set of shifts of the difference operator, the original problem is reduced to the boundary-value problem for differential equation with nonlocal boundary conditions.


About the authors

E. P. Ivanova

Peoples’ Friendship University of Russia (RUDN University); Moscow Aviation Institute (National Research University)

Author for correspondence.
Email: elpaliv@yandex.ru
Moscow, Russia

References

  1. Скубачевский А.Л. Краевые задачи для эллиптических дифференциально-разностных уравнений и их приложения// Усп. мат. наук. - 2016. -32, № 2. - С. 261-278.
  2. Ivanova E.P. On coercivity of differential-difference equations with incommensurable translations of arguments// J. Math. Sci. (N. Y.). - 2019. -239, № 6. - С. 802-816.
  3. Ivanova E.P. On smooth solutions of differential-Difference equations with incommensurable shifts of arguments// Math. Notes. - 2019. -105, № 1. - С. 140-144.
  4. Skubachevskii A.L. Elliptic functional differential equations and aplications. - Basel-Boston-Berlin: Birkhauser, 1997.

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