Oscillation of second-order functional differential equations with mixed nonlinearities and oscillatory potentials

摘要

In this paper, we study oscillation of second-order functional differential equations with mixed nonlinearities(p(t)x′(t))′+q(t)x(t-τ)+∑i=1nqi(t)|x(t-τ)|αisgnx(t-τ)=e(t),where τ⩾0, p(t)∈C1[0,∞), q(t),qi(t),e(t)∈C[0,∞), p(t)>0, α1>⋯>αm>1>αm+1>⋯>αn>0(n>m⩾1). Without assuming that q(t), qi(t) and e(t) are nonnegative, the results given in [Y.G. Sun, F.W. Meng, Interval criteria for oscillation of second-order differential equations with mixed nonlinearities, Appl. Math. Comput. 198 (2008) 375–381] have been extended to the aforementioned functional differential equation.