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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 6, pp. 860 – 864, June, 2010.
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Horbatenko, Y.V. Kostin-type criterion for abstract linear differential equations of arbitrary order in banach spaces. Ukr Math J 62, 997–1003 (2010). https://doi.org/10.1007/s11253-010-0408-5
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DOI: https://doi.org/10.1007/s11253-010-0408-5