2019
Том 71
№ 10

All Issues

Derfel' G. A.

Articles: 4
Article (Russian)

Asymptotic Discontinuity of Smooth Solutions of Nonlinear $q$-Difference Equations

Derfel' G. A., Romanenko Ye. Yu., Sharkovsky O. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 12. - pp. 1615-1629

We investigate the asymptotic behavior of solutions of the simplest nonlinear q-difference equations having the form x(qt+ 1) = f(x(t)), q> 1, tR +. The study is based on a comparison of these equations with the difference equations x(t+ 1) = f(x(t)), tR +. It is shown that, for “not very large” q> 1, the solutions of the q-difference equation inherit the asymptotic properties of the solutions of the corresponding difference equation; in particular, we obtain an upper bound for the values of the parameter qfor which smooth bounded solutions that possess the property \(\begin{array}{*{20}c} {\max } \\ {t \in [0,T]} \\ \end{array} \left| {x'(t)} \right| \to \infty \) as T→ ∞ and tend to discontinuous upper-semicontinuous functions in the Hausdorff metric for graphs are typical of the q-difference equation.

Article (Ukrainian)

Probabilistic method for a class of functional-differential equations

Derfel' G. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 10. - pp. 1322–1327

Article (Ukrainian)

Connection between the existence of summable and almost-periodic solutions of a class of differential-functional equations

Derfel' G. A., Shevelo V. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1987. - 39, № 4. - pp. 437–439

Article (Ukrainian)

Behavior of solutions of functional and differential-functional equations with several transformations of the independent variable

Derfel' G. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1982. - 34, № 3. - pp. 350–356