ASYMPTOTICS OF THE SPECTRUM FOR A FOURTH-ORDER DIFFERENTIAL OPERATOR WITH A SPECTRAL PARAMETER IN TWO BOUNDARY CONDITIONS

We consider the spectral problem a the fourth-order differential operator on a unit interval. In this case, two boundary conditions contain a spectral parameter. We assume that the coefficient of the differential expression is an absolutely continuous function. The main result is devoted to the sharp eigenvalue asymptotics at high energy. In addition, we obtain this result in the case of a smooth coefficient. This asymptotics shows an additional nonstandard effect, which is caused by the presence of a spectral parameter in the boundary conditions.