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Spectral properties of the family of even order differential operators with a summable potential. (English. Russian original) Zbl 1393.34034

Mosc. Univ. Math. Bull. 72, No. 4, 137-148 (2017); translation from Vestn. Mosk. Univ., Ser. I 72, No. 4, 3-15 (2017).
Summary: A boundary value problem for a higher order differential operator with separated boundary conditions is considered. The asymptotics of solutions of the corresponding differential equation for large values of the spectral parameter is studied. The indicator diagram of the equation for the eigenvalues is studied. The asymptotic behavior of eigenvalues and the formula for calculation of eigenfunctions of the studied operator is obtained in different sectors of the indicator diagram.

MSC:

34B09 Boundary eigenvalue problems for ordinary differential equations
34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators
34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
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