A maximum principle for nonlinear differential inequalities (Q1431940)

Sufficient conditions are obtained in terms of \(\psi\) and \(f\) such that a nontrivial solution \(y(t)\) of the nonlinear differential inequality \[ y(t)\{(\psi(y'(t)))'+f(t,y(t))\}\leq0\tag{\(*\)} \] does not have a double zero for any \(t\) and each of \(y(t)\) and \(y'(t)\) has at most finite number of zeros on any compact interval \([a, b]\). Moreover, some nonlinear maximum principles for (\(*\)) are established which generalize previous results of \textit{M. H. Protter} and \textit{H. F. Weinberger} [Maximum principles in differential equations Corr. reprint. New York etc.: Springer-Verlag (1967; Zbl 0549.35002)].