The application of similar operator method to investigation of spectral properties of differential operators of Sturm-Liouville type. (English. Russian original) Zbl 0756.34082

Katsaran, T. K.

Sov. Math. 35, No. 6, 73-76 (1991); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1991, No. 6(349), 72-75 (1991).

The operator \(L(\varepsilon)=-d^ 2/dt^ 2-\varepsilon b(t)\) under different (periodic, antiperiodic and Dirichlet) boundary conditions is studied in the space \(L_ 2(0,1)\). The aim of the paper is to obtain asymptotics of eigenvalues \(\lambda_ n(\varepsilon)\) of the problem considered as \(\varepsilon\to 0\) and \(n\to\infty\) under the only condition \(b\in L_ 2(0,1)\).

Reviewer: D.R.Yafaev (Rennes)

MSC:

34L20	Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators
34L05	General spectral theory of ordinary differential operators
34B24	Sturm-Liouville theory

Keywords:

asymptotics of eigenvalues