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J. Mikusiński, R. Sikorski, P. Antosik (1973)
Theory of distributions : the sequential approach
Differential Equations, Vol. 39, No. 3, 2003, pp. 353–361. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 3, 2003, pp. 328–336. Original Russian Text Copyright c 2003 by Mazurenko, Tatsii. ORDINARY DIFFERENTIAL EQUATIONS Solvability of a Nonhomogeneous Boundary Value Problem for a Di erential System with Measures V. V. Mazurenko and R. M. Tatsii National University \Lviv Polytechnics", Lviv, Ukraine Received August 1, 2001 INTRODUCTION We consider linear nonhomogeneous systems of di erential equations containing distributions as coecients. Descriptions of such systems typically contain some form of products of discontinuous functions by generalized derivatives of functions of bounded variation. These products do not always exist in the sense of distribution theory, and accordingly, di erent approaches to the de nition of a solution may give di erent results. A detailed review of the literature on this topic can be found in [1], where the main approaches to the de nition of a solution of the corresponding equations are also described. We also note the papers [2{6] dealing with the analysis of classes of linear and quasilinear di erential systems with measures whose solutions are treated in the sense of distribution theory, whereby their de nition (under some restrictions on the
Differential Equations – Springer Journals
Published: Oct 5, 2004
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