On Tykhonov's theorem for convergence of solutions of slow and fast systems.
On type of periodicity and ergodicity to a class of fractional order differential equations.
On unbounded positive solutions of nonlinear differential equations with oscillating coefficients
On uniqueness of solutions of differential equations
On vanishing at infinity of solutions of ordinary differential equations
On weak non-linearity of models of physical systems
One parameter family of linear difference equations and the stability problem for the numerical solution of ODEs.
One problem of D. S. Mitrinovič and its generalization
One-dimensional adaptive grid generation.
One-sided conditions for quasilinear Jacobi differential equations
One-step and Extrapolation Methods for Differential-Algebraic Systems.
Operational Calculi for the Euler Operator
2000 Mathematics Subject Classification: 44A40, 44A35A direct algebraic construction of a family of operational calculi for the Euler differential operator δ = t d/dt is proposed. It extends the Mikusiński's approach to the Heaviside operational calculus for the case when the classical Duhamel convolution is replaced by the convolution ...
Operational calculus and differential equations with infinitely smooth coefficients.
Operational calculus for the continuous Legendre transform with applications.
Operational identities for circular and hyperbolic functions and their generalizations.
Operational Methods in the Environment of a Computer Algebra System
This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.The presented research is related to the operational calculus approach and its representative applications. Operational methods are considered, as well as their...
Opial inequalities on time scales
We present a version of Opial's inequality for time scales and point out some of its applications to so-called dynamic equations. Such dynamic equations contain both differential equations and difference equations as special cases. Various extensions of our inequality are offered as well.
Opial's type inequalities on time scales and some applications
We prove some new Opial type inequalities on time scales and employ them to prove several results related to the spacing between consecutive zeros of a solution or between a zero of a solution and a zero of its derivative for second order dynamic equations on time scales. We also apply these inequalities to obtain a lower bound for the smallest eigenvalue of a Sturm-Liouville eigenvalue problem on time scales. The results contain as special cases some results obtained for second order differential...
Optimal Control of a Cancer Cell Model with Delay
In this paper, we look at a model depicting the relationship of cancer cells in different development stages with immune cells and a cell cycle specific chemotherapy drug. The model includes a constant delay in the mitotic phase. By applying optimal control theory, we seek to minimize the cost associated with the chemotherapy drug and to minimize the number of tumor cells. Global existence of a solution has been shown for this model and existence...
Optimal controllability of impulsive control systems.