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Oscillation criteria for a special class of 2n-order ordinary differential equations. (English) Zbl 0644.34024
The author considers the differential equation $$(1)\quad (-1)^ n(x^{\alpha}u^{(n)}(x))^{(n)}+q(x)u(x)=0,$$ $$x>0$$, where the function q is continuous. Equation (1) is said to be oscillatory if for each positive number a there exist positive numbers b and c with $$a<b<c$$ such that the equation (1) has a nontrivial solution u satisfying $$u^{(m)}(b)=u^{(m)}(c)=0$$, $$m=0,1,...,n-1$$. Sufficient conditions for the oscillation of equation (1) are given for $$\alpha =1,3,5,...,2n-1$$. They improve some previous results of the author in special cases.
Reviewer: J.Ohriska

##### MSC:
 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
##### Keywords:
oscillation of solutons
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##### References:
 [1] Ahlbrandt, Canad. J. Math. 33 pp 229– (1981) · Zbl 0462.47030 · doi:10.4153/CJM-1981-019-1 [2] und , Methoden der Mathematischen Physik, Springer-Verlag, Berlin–Heidelberg–New York 1968 · doi:10.1007/978-3-642-96050-5 [3] Fiedler, J. Diff. Equations 42 pp 155– (1981) [4] Fiedler, Nachr. 107 pp 187– (1982) [5] Direct methods of qualitative spectral analysis of singular differential operators, Jerusalem 1965 [6] Reid, Math. 13 pp 665– (1963)
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