On the solvability of boundary value problems for an abstract Bessel-Struve equation (Q2009909)

The paper deals with the abstract Bessel-Struve equation \[u''(t) + kt^{-1}\left(u'(t)-u'(0)\right) = A u(t), t>0,\] where \(A\) is a densely defined closed linear operator on a complex Banach space \(E\) and \(k>0\). Dirichlet and Neumann boundary value problems associated with this equations are considered, that are both not well-posed in general. Following the results from [\textit{A. V. Glushak}, Differ. Equ. 53, No. 7, 864--878 (2017; Zbl 1382.34065)] the author assumes that \(A\) is contained in the set of generators of integrated cosine operator functions and establishes further sufficient conditions on \(A\) and the boundary values for the unique solvability of both problems.