Interval oscillation criteria for a forced second order nonlinear ordinary differential equations with oscillatory potential.

*(English)*Zbl 1030.34034Summary: New oscillation criteria established for the forced second-order nonlinear equation with oscillatory potential

$${\left(p\left(t\right){y}^{\text{'}}\left(t\right)\right)}^{\text{'}}+q\left(t\right)f\left(y\left(t\right)\right)=g\left(t\right)$$

are different from the most known ones in the sense that they are based on the information only on a sequence of subintervals of $[{t}_{0},\infty )$, rather than on the whole half-line. Our results are of a high degree of generality and sharper than some previous results and handle the cases which are not covered by known results. Moreover, these results can also be applied to the extreme such as ${\int}_{{t}_{0}}^{\infty}q\left(s\right)ds=-\infty $.

##### MSC:

34C10 | Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory |