Interval criteria for oscillation of second-order differential equations with mixed nonlinearities

摘要

In this paper, we establish interval criteria for oscillation of the second order forced ordinary differential equations with mixed nonlinearities:(p(t)x′)′+q(t)x+∑i=1nqi(t)|x|αisgnx=e(t),where p(t), q(t), qi(t), e(t) are continuous functions defined on [0,∞), p(t) is positive and differentiable, α1 > ⋯ > αm > 1 > αm+1 > ⋯ > αn > 0(n > m ⩾ 1). No restriction is imposed on the potentials q(t), qi(t) and e(t) to be nonnegative.