On boundary-value problems for higher-order differential inclusions.
On bounded solutions of a linear differential equation with a nonlinear perturbation
On bounded solutions of nonlinear ordinary differential equations
On bounded time-dependent perturbations of operator cosine functions.
On boundedness and stability of solutions of nonlinear second order differential equations in Hilbert spaces
On Cauchy problemsfor fuzzydifferential equations.
On certain properties of linear iterative equations
An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator that generates an iterative equation of a general order in reduced normal form is also obtained and some other properties of iterative equations are established. An expression for the parameters of the source equation of the transformed equation under equivalence transformations is obtained,...
On Certain Properties of Soloutions of Second-Order Linear Differential Equations.
On characterization of the solution set in case of generalized semiflow
In the paper, a possible characterization of a chaotic behavior for the generalized semiflows in finite time is presented. As a main result, it is proven that under specific conditions there is at least one trajectory of generalized semiflow, which lies inside an arbitrary covering of the solution set. The trajectory mutually connects each subset of the covering. A connection with symbolic dynamical systems is mentioned and a possible numerical method of analysis of dynamical behavior is outlined....
On Clenshaws's Method and a Generalisation to Faber Series.
On complete solutions and complete singular solutions of second order ordinary differential equations
A complete solution of an implicit second order ordinary differential equation is defined by an immersive two-parameter family of geometric solutions on the equation hypersurface. We show that a completely integrable equation is either of Clairaut type or of first order type. Moreover, we define a complete singular solution, an immersive one-parameter family of singular solutions on the contact singular set. We give conditions for existence of a complete solution and a complete singular solution...
On complexity and motion planning for co-rank one sub-riemannian metrics
In this paper, we study the motion planning problem for generic sub-riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean [10, 11]), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic case, we study some non-generic generalizations in the analytic case.
On complexity and motion planning for co-rank one sub-Riemannian metrics
In this paper, we study the motion planning problem for generic sub-Riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean [CITE]), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic C∞ case, we study some non-generic generalizations in the analytic case.
On computer-aided solving differential equations and stability study of markets.
On conditions on right hand sides of differential relations
On conjugacy functions of second-order linear differential equations
On conjugacy of high-order linear ordinary differential equations.
On conjugate points of solutions of non-selfadjoint differential systems
On consistency, stability and convergence of staggered solution procedures
The simultaneous and staggered procedures of solving a partitioned form of a coupled system of ordinary differential equations are presented. Formulas for errors are compared. Counter-examples for convergence with a constant number of iterations at each time step are given.
On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)
One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.