2019
Том 71
№ 11

# Vityuk A. N.

Articles: 8
Brief Communications (Russian)

### Solvability of a Three-Point Boundary-Value Problem for a Second-Order Differential Inclusion

Ukr. Mat. Zh. - 2003. - 55, № 1. - pp. 132-137

We investigate the problem of the existence of solutions of a three-point boundary-value problem for a second order differential inclusion.

Brief Communications (Ukrainian)

### On the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side

Ukr. Mat. Zh. - 1999. - 51, № 11. - pp. 1562–1565

We prove a theorem on the existence of solutions of the differential inclusion $D_0^\alpha u(x) \in F(x,u(x)), u_{1 - \alpha } (0) = \gamma , \left( {u_{1 - \alpha } (x) = 1_0^{1 - \alpha } u(x)} \right),$ where $\alpha \in (0,1), D_0^\alpha u(x) \left( {1_0^{1 - \alpha } u(x)} \right)$ is the Riemann-Liouville derivative (integral) of order α, and the multivalued mappingF(x, u) is upper semicontinuous inu.

Article (Russian)

### Averaging in Volterra set-valued integral equations

Ukr. Mat. Zh. - 1995. - 47, № 12. - pp. 1622–1626

This paper is devoted to the justification of one averaging method for Volterra integral set-valued equations.

Brief Communications (Russian)

### On solutions of hyperbolic differential inclusions with nonconvex right-hand side

Ukr. Mat. Zh. - 1995. - 47, № 4. - pp. 531–534

The existence of a generalized solution with continuous derivativesu x ,u y is proved for the differential inclusionu xy F(x, y, u) with a nonconvex right-hand side satisfying the Lipschitz conditioninx, y, andu.

Article (Ukrainian)

### N. N. Bogolyubov's theorem for hyperbolic differential inclusions

Ukr. Mat. Zh. - 1987. - 39, № 5. - pp. 641–645

Article (Ukrainian)

### Solvability of a class of boundary-value problems for systems of hyperbolic differential equations

Ukr. Mat. Zh. - 1983. - 35, № 5. - pp. 611—613

Article (Ukrainian)

### Solvability and the difference method of solution of a boundary-value problem for a system of differential equations of the hyperbolic type

Ukr. Mat. Zh. - 1981. - 33, № 1. - pp. 50–53

Article (Ukrainian)

### Approximate solution of a generalized Cauchy problem by the method of averaging functional corrections

Ukr. Mat. Zh. - 1974. - 26, № 2. - pp. 152–160