We study an implicit inhomogeneous linear differential-difference equation in the module of formal generalized functions over a commutative ring. We prove the well-posedness of the equation and find the fundamental solution. We obtain a representation of a unique solution to the equation in the form of the convolution of the fundamental solution and a given formal generalized function. We also consider the inhomogeneous second order differential equation over an arbitrary commutative ring.
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Translated from Problemy Matematicheskogo Analiza 108, 2021, pp. 53-64.
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Gefter, S.L., Piven’, A.L. Implicit Linear Differential-Difference Equations in the Module of Formal Generalized Functions over a Commutative Ring. J Math Sci 255, 409–422 (2021). https://doi.org/10.1007/s10958-021-05381-8
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DOI: https://doi.org/10.1007/s10958-021-05381-8