Glushak, A. V.; Kononenko, V. I.; Shmulevich, S. D. 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 Cited in 7 Documents MSC: 34G10 Linear differential equations in abstract spaces 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations Keywords:second order differential equation; well-posedness of a Cauchy problem; abstract Euler-Poisson-Darboux equation PDF BibTeX XML Cite \textit{A. V. Glushak} et al., Sov. Math. 30, No. 6, 78--81 (1986; Zbl 0613.34047); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1986, No. 6(289), 55--56 (1986)