On transformations of two homogeneous linear second order differential equations of a general and of Sturm forms
The paper describes the general form of an ordinary differential equation of the order which allows a nontrivial global transformation consisting of the...
We present necessary and sufficient conditions for the existence of unbounded increasing solutions to ordinary differential equations with mean curvature operator. The results illustrate the asymptotic proximity of such solutions with those of an auxiliary linear equation on the threshold of oscillation. A new oscillation criterion for equations with mean curvature operator, extending Leighton criterion for linear Sturm-Liouville equation, is also derived.