New Oscillation Criteria for Second-Order Delay Differential Equations with Mixed Nonlinearities

Abstract EN

We establish new oscillation criteria for second-order delay differential equations with mixed nonlinearities of the form (p(t)x'(t))'+∑i=1npi(t)x(t-τi)+∑i=1nqi(t)|x(t-τi)|αisgn x(t-τi)=e(t), t≥0, where p(t), pi(t), qi(t), and e(t) are continuous functions defined on [0,∞), and p(t)>0, p′(t)≥0, and α1>⋯>αm>1>αm+1>⋯>αn>0.

No restriction is imposed on the potentials pi(t), qi(t), and e(t) to be nonnegative.

These oscillation criteria extend and improve the results given in the recent papers.

An interesting example illustrating the sharpness of our results is also provided.