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Oscillation and spectral properties of self-adjoint even order differential operators with middle terms. (English) Zbl 1072.34032

Summary: Oscillation and spectral properties of even-order selfadjoint differential operators of the form \[ L(y):=\frac{1}{w(t)}\sum_{k=0}^n (-1)^k \left(r_k(t)y^{(k)}\right)^{(k)},\quad r_n(t)>0,\;w(t)>0, \tag{L} \] are investigated. A particular attention is devoted to the fourth-order operators with a middle term, for which new (non)oscillation criteria are derived. Some open problems and perspectives of further research are discussed.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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