2019
Том 71
№ 11

# Ukrains’kyi Matematychnyi Zhurnal (Ukrainian Mathematical Journal)

Editor-in-Chief: A. M. Samoilenko
ISSN: 0041-6053, 1027-3190

Ukrains'kyi Matematychnyi Zhurnal (UMZh) was founded in May 1949. Journal is issued by Institute of Mathematics NAS of Ukraine. English version is reprinted in the Springer publishing house and called Ukrainian Mathematical Journal.

Ukrains'kyi Matematychnyi Zhurnal focuses on research papers in the principal fields of pure and applied mathematics. The journal is published monthly, each annual volume consists of 12 issues. Articles in Ukrainian, Russian and English are accepted for review.

UMZh indexed in: MathSciNet, zbMATH, Scopus, Web of Science, Google Scholar.

Impact Factor*: 0.189
*2015 Journal Citation Reports, Thomson Reuters

SCImago Journal Rank (SJR) 2015: 0.31; H-index: 13
Source Normalized Impact per Paper (SNIP) 2014: 0.605
Impact per Publication (IPP) 2014: 0.216

Mathematical Citation Quotient (MCQ) 2014: 0.22

## Latest Articles (November 2019)

Brief Communications (Russian)

### On the spectral properties of the one-dimensional Stark operator on the half-line

Ukr. Mat. Zh. - 2019. - 71, № 11. - pp. 1579-1584

UDC 517.9
We consider a one-dimensional Stark operator on a half-line with the Dirichlet boundary condition at zero. The asymptotic behavior of the eigenvalues at infinity is found.

Article (Russian)

### Asymptotic behavior of the solutions of boundary-value problems for singularly perturbed integro-differential equations

Ukr. Mat. Zh. - 2019. - 71, № 11. - pp. 1466-1479

UDC 517.928
We study the asymptotic behavior of the solutions of a boundary-value problem with boundary jumps for linear integrodifferential equations of the third order with small parameters at the two highest derivatives. The asymptotic convergence of the solution of a singularly perturbed integrodifferential boundary-value problem to the solution of the corresponding modified degenerate boundary-value problem is proved.

Article (English)

### A parabolic equation for the fractional Laplacian in the whole space: blow-up of nonnegative solutions

Ukr. Mat. Zh. - 2019. - 71, № 11. - pp. 1502-1518

UDC 517.9
The main aim of the present paper is to investigate under what conditions the nonnegative solutions blow-up for the parabolic problem $\dfrac{\partial u}{\partial t} = - (-\triangle)^{\frac{\alpha}{2}}u + \dfrac{c}{|x|^{\alpha}}u$ in $\mathbb{R}^{d}\times (0 , T),$ where $0<\alpha<\min(2,d),$ $(-\triangle)^{\frac{\alpha}{2}}$ is the fractional Laplacian on $\mathbb{R}^{d}$ and the initial condition $u_{0}$ is in $L^{2}(\mathbb{R}^{d}).$