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

We establish new oscillation criteria for second-order delay differential equations with mixed nonlinearities of the form (p(t)x'(t))' + Sigma(n)(i=1) p(i)(t)x(t-tau(i)) + Sigma(n)(i=1)q(i)(t)vertical bar x(t-tau(i))vertical bar(alpha i) sgnx(t-tau(i)) = e(t), t >= 0, where p(t),p(i)(t),q(i)(t), and e(t) are continuous functions defined on [0,infinity), and p(t) > 0, p'(t) = 0, and alpha(1) > ... > alpha(m) > 1 > am alpha(m+1) > ... > alpha(n) > 0. No restriction is imposed on the potentials p(i)(t), q(i)(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.