Problem without initial conditions for linear and almost linear degenerate operator differential equations - Dmytryshyn, Yu. B. (Ukrains’kyi Matematychnyi Zhurnal, 2009)
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.