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Zbl 0805.34009
Zavalishchin, S.T.
Impulse dynamic systems and applications to mathematical economics.
(English)
[J] Dyn. Syst. Appl. 3, No.3, 443-449 (1994). ISSN 1056-2176

The differential equation of the form (1) $dx/dt= f(x) + B(x,v) \cdot dv/dt$, $x(0) = x\sb 0$, is considered. Here $f : \bbfR\sp n \to \bbfR\sp n$, $B$ is an $(m \times n)$-matrix function and $v : \bbfR \to \bbfR\sp m$ is a time program. Suggesting the procedure for the multiplication of the discontinuous function $B(x(\cdot)$, $v(\cdot))$ and the impulse function $Dv$ the author gives the definition and the description for a weak solution of the equation (1). This approach allows to consider some mathematical market models with discontinuous current prices and to discuss stability and optimization problems.
[V.V.Obukhovskij (Voronezh)]
MSC 2000:
*34A37 Differential equations with impulses
91B50 Equilibrium in economics

Keywords: impulse equation; weak solution; mathematical market models with discontinuous current prices; stability and optimization problems

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