Impulse dynamic systems and applications to mathematical economics. (English) Zbl 0805.34009

Zavalishchin, S. T.

Dyn. Syst. Appl. 3, No. 3, 443-449 (1994).

The differential equation of the form (1) \(dx/dt= f(x) + B(x,v) \cdot dv/dt\), \(x(0) = x_ 0\), is considered. Here \(f : \mathbb{R}^ n \to \mathbb{R}^ n\), \(B\) is an \((m \times n)\)-matrix function and \(v : \mathbb{R} \to \mathbb{R}^ m\) 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.

Reviewer: V.V.Obukhovskij (Voronezh)

MSC:

34A37	Ordinary differential equations with impulses
91B50	General equilibrium theory

Keywords:

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