We study the problem without initial conditions for linear and almost linear degenerate operator differential equations in Banach spaces. The uniqueness of a solution of this problem is proved in the classes of bounded functions and functions with exponential behavior as t → –∞. We also establish sufficient conditions for initial data under which there exists a solution of the considered problem in the class of functions with exponential behavior at infinity.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 3, pp. 322–332, March, 2009.
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Dmytryshyn, Y.B. Problem without initial conditions for linear and almost linear degenerate operator differential equations. Ukr Math J 61, 383–398 (2009). https://doi.org/10.1007/s11253-009-0220-2
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DOI: https://doi.org/10.1007/s11253-009-0220-2