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In this paper, the asymptotics of the spectral data (eigenvalues and weightnumbers) are obtained for the higher-order differential operators withdistribution coefficients and separated boundary conditions. Additionally, weconsider the case when, for the two boundary value problems, some coefficientsof the differential expressions and of the boundary conditions coincide. Weestimate the difference of their spectral data in this case.  Although the asymptotic behaviour of spectral data is well-studied fordifferential operators with regular (integrable) coefficients, to the best ofthe author's knowledge, there were no results in this direction for thehigher-order differential operators with distribution coefficients (generalizedfunctions) in a general form. The technique of this paper relies on therecently obtained regularization and the Birkhoff-type solutions fordifferential operators with distribution coefficients. Our results haveapplications to the theory of inverse spectral problems as well as a separatesignificance.

Spectral data asymptotics for the higher-order differential operators with distribution coefficients