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Oscillation and nonoscillation criteria for second-order linear differential equations. (English) Zbl 0877.34029

The author considers the second-order differential equation \[ u''+ p(t)u=0,\tag{\(*\)} \] where \(p:[0,\infty)\to [0,\infty)\) is an integrable function. Sufficient conditions for oscillation and nonoscillation of equation \((*)\) are given which make some results of E. Hille [Trans. Am. Math. Soc. 64, 234-252 (1948; Zbl 0031.35402)] and Z. Nehari [Trans. Am. Math. Soc. 85, 428-445 (1957; Zbl 0078.07602)] more precise and even extend them in certain cases.

MSC:

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