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Oscillation criteria for certain forced second-order nonlinear differential equations. (English) Zbl 1061.34017
Summary: Two new oscillation criteria for forced second-order nonlinear differential equations of the form $$\left(r(t)\Psi\bigl(y(t)\bigr) \bigl|y' (t)\bigr|^{\alpha-1}y'(t)\right)'+q(t)f\bigl(y(t)\bigr)=e(t),\quad t \ge t_0,$$ are established. Our results are based on the information on a sequence of subintervals of $[t_0,\infty)$ only, rather than on the whole half-line. Our methodology is somewhat different from that of previous authors. The results presented here are much more general than a recent result of {\it W. T. Li} and {\it S. S. Cheng} [Appl. Math. Lett. 15, 259--263 (2002; Zbl 1023.34029)].

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