Kochubei A. N.
Linear and nonlinear heat equations on a $p$ -adic ball
Ukr. Mat. Zh. - 2018. - 70, № 2. - pp. 193-205
We study the Vladimirov fractional differentiation operator $D^{\alpha}_N,\; \alpha > 0,\; N \in Z$, on a $p$-adic ball B$B_N = \{ x \in Q_p : | x|_p \leq p^N\}$. To its known interpretations via the restriction of a similar operator to $Q_p$ and via a certain stochastic process on $B_N$, we add an interpretation as a pseudodifferential operator in terms of the Pontryagin duality on the additive group of $B_N$. We investigate the Green function of $D^{\alpha}_N$ and a nonlinear equation on $B_N$, an analog of the classical equation of porous medium.
Anatolii Mykhailovych Samoilenko (on his 80th birthday)
Antoniouk A. Vict., Berezansky Yu. M., Boichuk О. A., Gutlyanskii V. Ya., Khruslov E. Ya., Kochubei A. N., Korolyuk V. S., Kushnir R. M., Lukovsky I. O., Makarov V. L., Marchenko V. O., Nikitin A. G., Parasyuk I. O., Pastur L. A., Perestyuk N. A., Portenko N. I., Ronto M. I., Sharkovsky O. M., Tkachenko V. I., Trofimchuk S. I.
Ukr. Mat. Zh. - 2018. - 70, № 1. - pp. 3-6
Myroslav L’vovych Horbachuk (on his 75 th birthday)
Berezansky Yu. M., Gerasimenko V. I., Khruslov E. Ya., Kochubei A. N., Mikhailets V. A., Nizhnik L. P., Samoilenko A. M., Samoilenko Yu. S.
Ukr. Mat. Zh. - 2013. - 65, № 3. - pp. 451-454
Myroslav L’vovych Horbachuk (on his 70th birthday)
Adamyan V. M., Berezansky Yu. M., Khruslov E. Ya., Kochubei A. N., Kuzhel' S. A., Marchenko V. O., Mikhailets V. A., Nizhnik L. P., Ptashnik B. I., Rofe-Beketov F. S., Samoilenko A. M., Samoilenko Yu. S.
Ukr. Mat. Zh. - 2008. - 60, № 4. - pp. 439–442
Distributed-order calculus: An operator-theoretic interpretation
Ukr. Mat. Zh. - 2008. - 60, № 4. - pp. 478–486
Within the Bochner-Phillips functional calculus and Hirsch functional calculus, we describe the operators of distributed-order differentiation and integration as functions of the classical operators of differentiation and integration, respectively.
Strongly Nonlinear Differential Equations with Carlitz Derivatives over a Function Field
Ukr. Mat. Zh. - 2005. - 57, № 5. - pp. 669–678
In earlier papers the author studied some classes of equations with Carlitz derivatives for $\mathbb{F}_q$ -linear functions, which are the natural function field counterparts of linear ordinary differential equations. Here we consider equations containing self-compositions $u \circ u ... \circ u$ of the unknown function. As an algebraic background, imbeddings of the composition ring of $\mathbb{F}_q$ -linear holomorphic functions into skew fields are considered.
The liouville operator
Ukr. Mat. Zh. - 1991. - 43, № 12. - pp. 1664–1671
Extension theory for symmetric operators and boundary value problems for differential equations
Gorbachuk M. L., Gorbachuk V. I., Kochubei A. N.
Ukr. Mat. Zh. - 1989. - 41, № 10. - pp. 1299–1313
One-dimensional point interactions
Ukr. Mat. Zh. - 1989. - 41, № 10. - pp. 1391–1395
Generalized solutions of operator-differential equations
Ukr. Mat. Zh. - 1985. - 37, № 6. - pp. 703–707
Self-adjointness of a differential operator with unbounded singular operator coefficient
Ukr. Mat. Zh. - 1976. - 28, № 4. - pp. 453–462
On the self-adjointness and on the nature of the spectrum of certain classes of abstract differential operators
Ukr. Mat. Zh. - 1973. - 25, № 6. - pp. 811—815
On best approximation in normed modules
Ukr. Mat. Zh. - 1973. - 25, № 1. - pp. 103—106