We study the simplest implicit linear inhomogeneous differential equation in an arbitrary vector space. We find the fundamental solution in the space of formal generalized functions and obtain a representation of a unique solution as the convolution of the fundamental solution and a given generalized function.
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Dedicated to Professor N. N. Uraltseva
Translated from Problemy Matematicheskogo Analiza 78, January 2015, pp. 47-55.
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Gefter, S.L., Stulova, T.E. Fundamental Solution of the Simplest Implicit Linear Differential Equation in a Vector Space. J Math Sci 207, 166–175 (2015). https://doi.org/10.1007/s10958-015-2363-z
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DOI: https://doi.org/10.1007/s10958-015-2363-z