A maximum principle for second order nonlinear differential inequalities and its applications Original Research Article

Let y(t) be a nontrivial solution of the second order differential inequality y(t){(r(t)y′(t))′ + ƒ(t,y(t))} ⩽ 0 We show that the zeros of y(t) are simple; y(t) and y′(t) have at most finite number of zeros on any compact interval [a, b] under suitable conditions on r and f. Using the main result, we establish some nonlinear maximum principles and a nonlinear Levinʹs comparison theorem, which extend some results of Protter, Weinberger, and Levin.