A MAXIMUM PRINCIPLE FOR 2ND-ORDER NONLINEAR DIFFERENTIAL-INEQUALITIESAND ITS APPLICATIONS

Let y(t) be a nontrivial solution of the second order differential ine quality y(t){(r(t)y'(t))' + f(t,y(t))} less than or equal to 0. We sho w that the zeros of y(t) are simple; y(t) and y'(t) have at most finit e number of zeros on any compact interval [a,b] under suitable conditi ons on r and f. Using the main result, we establish some nonlinear max imum principles and a nonlinear Levin's comparison theorem, which exte nd some results of Protter, Weinberger, and Levin.