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Integral averages and oscillation of second-order nonlinear differential equations. (English) Zbl 0989.34025
Here, the equation $$[a(t)\psi(x(t))x'(t)]'+q(t)f(x(t))=0 \tag E$$ with $a\in C^1([t_0,\infty);(0,\infty))$, $q\in C([t_0,\infty);\bbfR)$, $\psi,f\in C^1(\bbfR;\bbfR)$, $\psi(x)>0$, $xf(x)>0$ and $f'(x)\geq 0$ for $x\neq 0$ is studied. The author presents new oscillation criteria for equation (E) in both sublinear and superlinear cases. The main tool is the method of weighted averages and the function $H(t,s)$ established by {\it Ch. G. Philos} [Arch. Math. 53, 482-492 (1989; Zbl 0661.34030)].

34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34A34Nonlinear ODE and systems, general
Full Text: DOI
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