New interval oscillation criteriafor second-order functional differentialequations with nonlinear damping : Open Mathematics

摘要

This paper concerns the oscillation problem of second-order nonlinear damped ODE with functionalterms.We give some new interval oscillation criteria which is not only based on constructing a lower solution ofa Riccati type equation but also based on constructing an upper solution for corresponding Riccati type equation.We use a recently developed pointwise comparison principle between those lower and upper solutions to obtain ourresults. Some illustrative examples are also provided to demonstrate our results.