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

Michael V. Basin

International Journal of Stochastic Analysis, 1996, vol. 9, 1-10

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.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:108243

DOI: 10.1155/S1048953396000019

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