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Impulse dynamic systems and applications to mathematical economics. (English) Zbl 0805.34009
The differential equation of the form (1) dx/dt=f(x)+B(x,v)·dv/dt, x(0)=x 0 , is considered. Here f: n n , B is an (m×n)-matrix function and v: m is a time program. Suggesting the procedure for the multiplication of the discontinuous function B(x(·), v(·)) 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.
MSC:
34A37Differential equations with impulses
91B50General equilibrium theory in economics