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In the paper, we consider distribution of eigenvalues of a third-order differential operator with nonlocal boundary conditions on a segment. The characteristic operator of the considered spectral problem is an entire function that has an integral representation. Countability and asymptotics of zeros for an entire function on the complex plane in sectors with a small span along the imaginary axis is proved.

advances in difference equations

On zeros of the characteristic determinant of the spectral problem for a third-order differential operator on a segment with nonlocal boundary conditions