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Zbl 0913.34022
Constantin, Adrian
A general-weight Sturm-Liouville problem. (English)
[J] Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 24, No.4, 767-782 (1997). ISSN 0391-173X

The spectrum of the general Sturm-Liouville problem $$y''=q(x)y + \lambda m(x) y$$ is studied when the functions $m$ and $q$ are continuous and periodic of period one. Under some natural conditions the author extends the well-known results on the distribution of the spectrum for Hill's equation [see, e.g. {\it G. Birkhoff} and {\it G. C. Rota}, Ordinary differential equations, J. Wiley \& Sons, New York (1989)] to the general case. The distribution and the nature of periodic, anti-periodic, Dirichlet and Neumann spectra for the above equation are established.
[L.P.Lebedev (Rostov-na-Donu)]

MSC 2000:: *34B24 Sturm-Liouville theory

Keywords: spectrum; Sturm-Liouville problem; ordinary differential equation

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