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Oscillation of second order linear delay differential equations. (English) Zbl 1057.34077

This paper deals with the existence of oscillatory solutions of the equation \[ u''(t)+ p(t)u(\tau(t))= 0, \] where \(p:\mathbb{R}_+\to \mathbb{R}_+\) is locally integrable, \(\tau:\mathbb{R}_+\to \mathbb{R}\) is continuous, \(\tau(t)\leq t\) for \(t\geq 0\), \(\tau(t)\to+\infty\) and \[ \text{mes}\{s\geq t\mid p(s)> 0\}> 0\quad\text{for }t\geq 0. \] Here, mes denotes the Lebesgue measure on the real line. A number of known results is improved.

MSC:

34K11 Oscillation theory of functional-differential equations
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