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Oscillation criteria for second-order sublinear differential equation. (English) Zbl 0955.34022
The author establishes oscillation criteria for the second-order nonlinear differential equation $$ [a(t)\psi(x(t))x'(t)]'+q(t)f(x(t))=0, \tag{*} $$ with $a\in C^1([t_0,\infty);(0,\infty))$, $q\in C^1([t_0,\infty);\bbfR)$ (no restriction on its sign), $\psi\in C^1(\bbfR;\bbfR)$, $f\in C^1(\bbfR;\bbfR)$ such that $xf(x)>0$, $f'(x)\geq 0$ for $x\ne 0$ and $$ \int_{0+}\frac{\psi(u)}{f(u)}du<\infty,\quad \int_{0-}\frac{\psi(u)}{f(u)}du<\infty. $$ The oscillation results established here involve the average behavior of the integral of the alternating coefficient $q$ and are in terms of a parameter function $H(t,s)$. The obtained results generalize oscillation criteria of {\it H. J. Li} and {\it C. C. Yeh} [Dyn. Syst. Appl. 6, No. 4, 529-534 (1997; Zbl 0888.34024)] and of {\it Ch. G. Philos} [Differ. Integral Equ. 4, No. 1, 205-213 (1991; Zbl 0721.34026)].

MSC:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
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References:
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