# Horodets’kyi V. V.

### Nonlocal multipoint (in time) problem for evolutionary pseudodifferential equations with analytic symbols in spaces of type $W$

Horodets’kyi V. V., Martynyuk O. V., Petryshyn R. I.

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 9. - pp. 1208-1226

UDC 517.956

The correct solvability of a nonlocal multipoint (in time) problem for the evolution equations with differentiation operators of infinite order is established for an infinite time interval and an initial function, which is an element of the space of generalized functions of the type $ W'$.
The properties of the fundamental solution and the behavior of the solution as $ t \to + \infty $ are investigated.

### A problem for one class of pseudodifferential evolutionary equations multipoint in the time variable

Horodets’kyi V. V., Petryshyn R. I., Verezhak A. P.

Ukr. Mat. Zh. - 2018. - 70, № 3. - pp. 337-355

We establish the correct solvability of the multipoint (in the time variable) problem for the evolution equation with operator of differentiation of infinite order in generalized $S$-type spaces. The properties of the fundamental solution of this problem and the behavior of the solution $u(t, x)$ as $t \rightarrow +\infty$ are investigated.

### Multipoint (in Time) Problem for One Class of Evolutionary Pseudodifferential Equations

Drin Ya. M., Horodets’kyi V. V.

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 619–633

We establish the well-posed solvability of a nonlocal multipoint (in time) problem for the evolution equations with pseudodifferential operators of infinite order.

### Nonlocal Problem Multipoint in Time for the Evolutionary Equations with Pseudo-Bessel Operators with Variable Symbols

Horodets’kyi V. V., Martynyuk O. V.

Ukr. Mat. Zh. - 2014. - 66, № 2. - pp. 159–175

We study the properties of the fundamental solution of a nonlocal problem multipoint in time for the evolutionary equations with pseudo-Bessel operators constructed on variable symbols. The solvability of this problem is proved in the class of bounded continuous functions even on ℝ. The integral representation of solutions is established.

### Correct Solvability of a Nonlocal Multipoint (in Time) Problem for One Class of Evolutionary Equations

Horodets’kyi V. V., Martynyuk O. V., Petryshyn R. I.

Ukr. Mat. Zh. - 2013. - 65, № 3. - pp. 339-353

We study properties of a fundamental solution of a nonlocal multipoint (with respect to time) problem for evolution equations with pseudo-Bessel operators constructed on the basis of constant symbols. The correct solvability of this problem in the class of generalized functions of distribution type is proved.

### Summation of formal Fourier series by methods of Gauss-Weierstrass type

Ukr. Mat. Zh. - 1989. - 41, № 6. - pp. 831-835

### Some stabilization theorems for solutions of the Cauchy problem for Shilov-parabolic systems in classes of generalized functions

Ukr. Mat. Zh. - 1988. - 40, № 1. - pp. 43–48

### Convergence of series of independent Gaussian operators

Gorbachuk M. L., Horodets’kyi V. V.

Ukr. Mat. Zh. - 1984. - 36, № 4. - pp. 500 – 502