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Autor: Derr, V. Ya.

The present book gives a systematic overview of function theory and the theory of Stieltjes integral. In particular, we give a detailed account of the theory of functions of bounded variation and of the theory of regulated functions (= functions havi

Externí odkaz: http://arxiv.org/abs/2405.12887

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On uniform continuous dependence of solution of Cauchy problem on a parameter

Autor: Derr, V. Ya.

Suppose that an $n$-dimensional Cauchy problem \frac{dx}{dt}=f(t,x,\mu) (t \in I, \mu \in M), x(t_0)=x^0 satisfies the conditions that guarantee existence, uniqueness and continuous dependence of solution x(t,t_0,\mu) on parameter \mu in an open set

Externí odkaz: http://arxiv.org/abs/1205.0208

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Disconjugacy of a second order linear differential equation and periodic solutions

Autor: Derr, V. Ya.

The present paper is devoted to a new criterion for disconjugacy of a second order linear differential equation. Unlike most of the classical sufficient conditions for disconjugacy, our criterion does not involve assumptions on the smallness of the c

Externí odkaz: http://arxiv.org/abs/1005.5646

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The theory of disconjugacy for a second order linear differential equation

Autor: Derr, V. Ya.

This is an introduction to the theory of disconjugacy for a second order linear differential equation. We give new proofs of some of basic results and obtain new sufficient conditions for disconjugacy (in particular, on the whole real axis).

Externí odkaz: http://arxiv.org/abs/0811.4636

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The space of distributions with discontinuous test functions and a family of zero-sum games with discontinuous payoffs

Autor: Derr, V., Kinzebulatov, D.

In the present paper we consider one class of zero-sum games with discontinuous payoffs which may have no solutions in the sets of pure or mixed strategies. We show that, however, the solution always exists in the set of so-called $\mathcal R'$-mixed

Externí odkaz: http://arxiv.org/abs/math/0606126

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Distributions with dynamic test functions and multiplication by discontinuous functions

Autor: Derr, V., Kinzebulatov, D.

As follows from the Schwartz Impossibility Theorem, multiplication of two distributions is in general impossible. Nevertheless, often one needs to multiply a distribution by a discontinuous function, not by an arbitrary distribution. In the present p

Externí odkaz: http://arxiv.org/abs/math/0603351

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