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A singular abstract Cauchy problem. (English. Russian original) Zbl 0613.34047
Sov. Math. 30, No. 6, 78-81 (1986); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1986, No. 6(289), 55-56 (1986).
The author is concerned with the well-posedness of a Cauchy problem associated to the abstract Euler-Poisson-Darboux equation \[ u''(t)+(k/t)u'(t)=Au(t),\quad t>0 \] in a Banach space E. Here u is a function with values in E, \(k\in R\), and A denotes a closed linear operator in E that generates a strongly continuous cosine family.
Reviewer: S.Aizicovici

34G10 Linear differential equations in abstract spaces
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations