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Oscillation criteria for second order nonlinear differential equations with integrable coefficients. (English) Zbl 0760.34032

The paper deals with oscillation properties of the nonlinear second order differential equation \(y''+a(t)f(y)=0\). In addition to the usual assumptions on the nonlinearity \(f(f\in C^1,\;f'\geq 0,\;yf(y)>0\) for \(y\ne 0)\) it is assumed that the function \(a(t)\) is integrable, i.e., the improper integral \(\int^\infty_ta(s)\,ds=:A(t)\) exists and is finite for each \(t\ge 0\). The oscillation criteria of W. J. Coles [Ann. Mat. Pura Appl., IV.Ser. 82, 123–133 (1969; Zbl 0188.15304)] and G. J. Butler [Indian J. Math. 24, 1–7 (1982; Zbl 0532.34024)] are extended to a more general equation without the sign restriction on the function \(A(t)\).

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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