# 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.

## Latest Articles (September 2017)

### Total differential

↓ Abstract

Ukr. Mat. Zh. - 2017. - 69, № 9. - pp. 1250-1256

We present necessary and sufficient conditions for a continuous differential form to be the total differential.

### Reconstruction of the Sturm – Liouville operator with nonseparated boundary conditions and a spectral parameter in the boundary condition

Ibadzadeh Ch. G.,, Nabiev I.M.

↓ Abstract

Ukr. Mat. Zh. - 2017. - 69, № 9. - pp. 1217-1223

We study the inverse problem for the Sturm – Liouville operator with nonseparated boundary conditions one of which contains a spectral parameter. The uniqueness theorem is presented and sufficient conditions for the solvability of the inverse problem are obtained.

### Exact solutions of the nonliear equation $u_{tt} = = a(t) uu_{xx} + b(t) u_x^2 + c(t) u $

Barannik A. F., Barannik A. F., Yuryk I. I.

↓ Abstract

Ukr. Mat. Zh. - 2017. - 69, № 9. - pp. 1180-1186

Ans¨atzes that reduce the equation$u_{tt} = = a(t) uu_{xx} + b(t) u_x^2 + c(t) u $ to a system of two ordinary differential equations are defined. Also it is shown that the problem of constructing exact solutions of the form $u = \mu 1(t)x_2 + \mu 2(t)x\alpha , \alpha \in \bfR$, to this equation, reduces to integrating of a system of linear equations $\mu \prime \prime 1 = \Phi 1(t)\mu 1, \mu \prime \prime 2 = \Phi 2(t)\mu 2$, where $\Phi 1(t)$ and \Phi 2(t) are arbitrary predefined functions.