Abstract
We examine solvability questions of inverse problems on recovering a right-hand side of a special form in an operator-differential equation of the first order defined in some Hilbert space. An operator at the derivative with respect to time can have a nontrivial kernel and the spectrum of the corresponding linear pencil can contain unbounded subsets of the right and left half-planes. The boundary data are the values of a solution at the initial and final moments of time. Existence and uniqueness theorems are obtained under some conditions for the data.
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