Abstract
Saratov State Law Academy, Russia, 410056, Saratov, Volskaya st., 1, Oksana_Parfilova@mail.ruA class of strongly irregular pencils of ordinary differential operators of second order with constant coefficients is considered. Theroots of the characteristic equation of the pencils from this class are supposed to lie on a straight line coming through the originand on the both side of the origin. Exact interval on which the system of eigenfunctions is 2-fold complete in the space of squaresummable functions is finded.Key words: quadratic pencil, second order pencil, pencil of ordinary differential operators, two-point boundary conditions,homogeneous differential expression with constant coefficients, completeness of the system of eigenfunctions, non-completenessof the system of eigenfunctions.
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