2019
Том 71
№ 7

# Antypko I. I.

Articles: 2
Brief Communications (Russian)

### A theorem of the Phragmén-Lindelöf type for solutions of an evolution equation of the second order with respect to time variable

Ukr. Mat. Zh. - 1998. - 50, № 5. - pp. 724–731

We consider a solution u(x, t) of the general linear evolution equation of the second order with respect to time variable given on the ball Π(T) = {(x,t): xε R n, t ε [0, T]} and study the dependence of the behavior of this solution on the behavior of the functions at infinity.

Brief Communications (Ukrainian)

### Boundary-value problem in an infinite layer

Ukr. Mat. Zh. - 1995. - 47, № 3. - pp. 400–402

We establish necessary and sufficient conditions for a nonlocal two-point boundary-value problem in an infinite layer for the equation $$\frac{{\partial ^2 u(x,t)}}{{\partial t^2 }} + P\left( {\frac{\partial }{{\partial x}}} \right)\frac{{\partial u(x + h_1 ,t)}}{{\partial t}} + Q\left( {\frac{\partial }{{\partial x}}} \right)u(x + h_2 ,t) = 0,$$ whereP(s) andQ(s) are polynomials ins∈ℂ m with constant coefficients, to have infinite type and be degenerate.