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Linear differential equations of the second order with elementary basic central dispersions. (English) Zbl 0581.34036

This paper investigates differential equations of the type (q) \(y''=q(t)y\), \(q\in C^ 0({\mathbb{R}})\), \(({\mathbb{R}}:=(-\infty,\infty))\) being oscillatory on \({\mathbb{R}}\) (i.e. \(\pm \infty\) are the cluster points of zeros of any (nontrivial) solution of (q)). Equation (q) is often assumed such that its basic central dispersion is elementary. This property occurs e.g. in equation (q) whose coefficient q is a \(\pi\)-periodic function (on \({\mathbb{R}})\). Naturally, not every equation (q) with an elementary basic central dispersion has a \(\pi\)-periodic coefficient. The object of this paper is to investigate conditions under which (q) with an elementary basic central dispersion has a \(\pi\)-periodic coefficient q.

MSC:

34C99 Qualitative theory for ordinary differential equations
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References:

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