On an infinite-dimensional differential equation in vector distribution with discontinuous regular functions in a right hand side
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.
Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.