Description of a class of multivalued differential equations with almost weakly stable trivial solution
Generalized functional-differential equations of neutral type
Existence, uniqueness and continuous dependence of solutions of differential equations in Banach space
Stochastic differential inclusions
The definition and some existence theorems for stochastic differential inclusions depending only on selections theorems are given.
Properties of generalized set-valued stochastic integrals
The paper is devoted to properties of generalized set-valued stochastic integrals defined in [10]. These integrals generalize set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4]. Up to now we were not able to construct any example of set-valued stochastic processes, different on a singleton, having integrably bounded set-valued integrals defined in [4]. It was shown by M. Michta (see [11]) that in the general case set-valued stochastic integrals defined by E.J. Jung...
Continuous selection theorems
Continuous approximation selection theorems are given. Hence, in some special cases continuous versions of Fillipov's selection theorem follow.
Stochastic differential inclusions
The definition and some existence theorems for stochastic differential inclusion dZₜ ∈ F(Zₜ)dXₜ, where F and X are set valued stochastic processes, are given.
Some remarks on boundary value problem for differential inclusions
Some sufficient conditions for the existence of solutions to boundary value problem for differential inclusions are given.
Controllability theorem for nonlinear dynamical systems
Some sufficient conditions for controllability of nonlinear systems described by differential equation ẋ = f(t,x(t),u(t)) are given.
Viability theorems for stochastic inclusions
Sufficient conditions for the existence of solutions to stochastic inclusions beloning to a given set K of n-dimensional cádlág processes are given.
Tightness of Continuous Stochastic Processes
Some sufficient conditins for tightness of continuous stochastic processes is given. It is verified that in the classical tightness sufficient conditions for continuous stochastic processes it is possible to take a continuous nondecreasing stochastic process instead of a deterministic function one.
Strong and weak solutions to stochastic inclusions
Existence of strong and weak solutions to stochastic inclusions and , where p and q are certain random measures, is considered.
Boundedness of set-valued stochastic integrals
The paper deals with integrably boundedness of Itô set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4], where has not been proved that this integral is integrably bounded. The problem of integrably boundedness of the above set-valued stochastic integrals has been considered in the paper [7] and the monograph [8], but the problem has not been solved there. The first positive results dealing with this problem due to M. Michta, who showed (see [11]) that there are bounded...
On the nonconvergence of successive approximations in the theory of the equation
On some applications of Bogoliubov method for hyperbolic equations
The Orlicz type theorem for differential-integral equations with a lagging argument
Approximation theorem for set-valued functions
La presente Nota contiene la dimostrazione di un teorema di approssimazione per funzioni a valori insiemi compatti convessi. Si dimostra che ogni funzione soddisfacente condizioni di tipo Carathéodory può approssimarsi con una localmente lipschitziana.
Selection theorems for stochastic set-valued integrals
Some special selections theorems for stochastic set-valued integrals with respect to the Lebesgue measure are given.
Description of a class of differential equations with set-valued solutions. Nota II
Nella presente Nota II diamo la dimostrazione del teorema di tipo Orlicz concernente equazioni differenziali con soluzioni a valori, che sono insiemi compatti convessi.
Description of a class of differential equations with set-valued solutions. Nota I
Nelle presenti Note (I e II) proviamo il teorema di tipo Orlicz per equazioni differenziali con soluzioni a valori che sono insiemi compatti convessi. Questa Nota contiene le definizioni di base e la dimostrazione della completezza di uno spazio metrico fondamentale.
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