Michael V. Basin, "On an infinite-dimensional differential equation in vector distribution with discontinuous regular functions in a right hand side", International Journal of Stochastic Analysis, vol. 9, Article ID 108243, 10 pages, 1996. https://doi.org/10.1155/S1048953396000019
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.
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