**Oscillation and spectral properties of self-adjoint even order differential operators with middle terms**

**O. Dosly**, Department of Mathematics, Masaryk University, Brno, Czech Republic

E. J. Qualitative Theory of Diff. Equ., Proc. 7'th Coll. Qualitative Theory of Diff. Equ., No. 7. (2004), pp. 1-21.

Communicated by J. R. Graef.
| Received on 2003-09-29 Appeared on 2004-08-31 |

**Abstract: **Oscillation and spectral properties of even order self-adjoint 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.

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