Abstract
A necessary condition for the existence and uniqueness of mild solutions of first- and second-order differential equations on the real line is given. It is known that the first-order problem is related to the operator equation AX − XD = −δ0. Here, it is shown how the second-order problem on the real line is connected to the operator equation AX − XD2 = −δ0 and also to some other operator equations.
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