Differential equations with bounded positive Green’s functionsand generalized Aizerman’s hypothesis

We derive conditions for the positivity and boundedness of the Green functions of the higher order linear nonautonomous ODE. By virtue of these conditions, the existence of positive solutionsfor a class of nonlinear equations is proved. In addition, upper and lower estimates for the Green functionsare established. Moreover, it is shown that nonlinear equations, having separated nonautonomous linear parts, satisfy the generalized Aizerman hypothesis on absolute stability, if they have the positive Green functions.