A maximum principle for nonlinear differential inequalities

AbstractIn this paper, we consider the following nonlinear differential inequality: y(t){ψ(y′(t))′ + f(t,y(t))}⩽0, where ψ and f satisfy some suitable conditions. Let y(t) be a nontrivial solution of (E1). 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]. Moreover, we establish some nonlinear maximum principles, which extend some results of Protter and Weinberger