Monotone solutions of second-order nonlinear differential equations
Necessary and sufficient conditions are obtained for the existence of a positive nondecreasing solution to equations of the form \[ [r(t)(y'(t))^{\alpha }]'+q(t)(y(t))^{\alpha }=0, \] where \(\alpha \) is a positive number and \(r, q\) are continuous functions. As applications, some comparison theorems are derived.
nonlinear differential equation of second order
scientific article; zbMATH DE number 1540371