Journal of Applied Mathematics and Stochastic Analysis 
Volume 9 (1996), Issue 1, Pages 1-10
doi:10.1155/S1048953396000019

On an infinite-dimensional differential equation in vector distribution with discontinuous regular functions in a right hand side

Michael V. Basin1

 1Institute of Control Science, Moscow, Russia
236-1-135,Matveevskaya ul., Moscow 119517, Russia
Received 1 April 1995; Revised 1 September 1995

Abstract

An infinite-dimensional differential equation in vector distribution in a Hilbert space is studied in case of an unbounded operator and discontinuous regular functions in a right-hand side. A unique solution (vibrosolution) is defined for such an equation, and the necessary and sufficient existence conditions for a vibrosolution are proved. An equivalent equation with a measure, which enables us to directly compute jumps of a vibrosolution at discontinuity points of a distribution function, is also obtained. The application of the obtained results to control theory is discussed in the conclusion.