On oscillation properties of delay differential equations with positive and negative coefficients

AbstractFor a scalar delay differential equation ẋ(t)+a(t)xh(t)−b(t)xg(t)=0,a(t)⩾0,b(t)⩾0,h(t)⩽t,g(t)⩽t, a connection between the following properties is established: nonoscillation of the differential equation and the corresponding differential inequalities, positiveness of the fundamental function and existence of a nonnegative solution for a certain explicitly constructed nonlinear integral inequality. A comparison theorem and explicit nonoscillation and oscillation results are presented