Kostin-type criterion for abstract linear differential equations of arbitrary order in banach spaces - Horbatenko, Ya. V. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
We consider linear differential equations with operator coefficients in a Banach space. We construct necessary and sufficient conditions for the well-posedness of the Cauchy problem for these equations of arbitrary order that are analogous to the Kostin conditions for incomplete equations of the second order.