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Asymptotic behaviour of eigenvalues for the discontinuous boundary value problem with functional-transmission conditions. (English) Zbl 1013.34079

Summary: Here, the boundary value problem with eigenvalue parameter generated by a differential equation with discontinuous coefficients and boundary conditions, that contain not only endpoints of the considered interval, but also points of discontinuity and abstract linear functionals, is investigated. So, the problem is not pure a boundary value problem. The authors single out a class of linear functionals and find simple algebraic conditions on the coefficients, which guarantee the existence of an infinite number of eigenvalues. Also, asymptotic formulas for the eigenvalues are found.

MSC:

34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators
34B07 Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter
34B24 Sturm-Liouville theory
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