Abstract
The article deals with the problem of existence of generalized solutions to linear differential equation with a generalized coefficient Q which coincides with a given rational function q on the complement to the set of poles of q. To introduce a generalized solution, we consider approximations of the coefficient Q by a family of smooth functions. Then, the generalized solution is the limit of the solutions to approximating equations. A principal difference from the classical theory here is that even such simplest equations with singular coefficient Q may not have the solution. The main result is the description of those Q from the class considered for whom a generalized solution does exist.
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Dedicated to Eightieth Anniversary of the Birth of Nikolai Karapetiants—a remarkable mathematician and person.
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Antonevich, A.B., Kuzmina, E.V. ON GENERALIZED SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS OF THE FIRST ORDER. J Math Sci 266, 26–41 (2022). https://doi.org/10.1007/s10958-022-05871-3
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DOI: https://doi.org/10.1007/s10958-022-05871-3