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

Abstract

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, wherep(t),pi(t),qi(t), ande(t)are continuous functions defined on[0,∞), andp(t)>0,p′(t)≥0, andα1>⋯>αm>1>αm+1>⋯>αn>0. No restriction is imposed on the potentialspi(t),qi(t), ande(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.