Qualitative theory of half-linear second order differential equations

Qualitative Theory of Half-linear Second Order Differential Equations

Some recent results concerning properties of solutions of the half-linear second order differential equation (∗) (r(t)Φ(x′))′ + c(t)Φ(x) = 0, Φ(x) := |x|p−2x, p > 1, are presented. A particular attention is paid to the oscillation theory of (∗). Related problems are also discussed.

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty

Oscillation of Second Order Half-linear Differential Equations with Damping

This paper is concerned with a class of second order half-linear damped differential equations. Using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of the existing results. 2000 Mathematics Subject Classification: 34A30, 34C10.

A Linearization Method in Oscillation Theory of Half-linear Second-order Differential Equations

Using inequalities for a certain function appearing in the half-linear version of Picone’s identity, we show that oscillatory properties of the half-linear second-order differential equation (r(t)Φ(x′))′ + c(t)Φ(x) = 0, Φ(x) = |x|p−2x, p > 1, can be investigated via oscillatory properties of a certain associated second-order linear differential equation. This linear equation plays the role of a...

Second Order Linear and Nonlinear Differential Equations'