On nonoscillatory solutions of fourth-order differential equations (Q2784669)

The authors investigate asymptotic properties of nonoscillatory solutions to the fourth-order differential equation NEWLINE\[NEWLINE y^{(4)}-(q(t)y')'+r(t)f(y)=0, NEWLINE\]NEWLINE where \(q, r\) are continuous functions on \([0,\infty)\), \(r(t)\geq 0\) and \(f(u)u>0\) for \(u\neq 0\). A classification of all nonoscillatory solutions is introduced according to the signs or oscillatory character of their derivatives and sufficient conditions on the nonlinearity \(f\) are given which ensure that one or more of these classes of solutions are empty.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00016].