Ordinary differential equations in the oscillation theory of partial half-linear differential equation

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.

Forced oscillation of super-half-linear impulsive differential equations

By using a Picone type formula in comparison with oscillatory unforced half-linear equations, we derive new oscillation criteria for second order forced super-half-linear impulsive differential equations having fixed moments of impulse actions. In the superlinear case, the effect of a damping term is also considered. c © 2007 Elsevier Ltd. All rights reserved.

Conditional Oscillation of Half-linear Differential Equations with Periodic Coefficients

We show that the half-linear differential equation (∗) [ r(t)Φ(x′) ]′ + s(t) tp Φ(x) = 0 with α-periodic positive functions r, s is conditionally oscillatory, i.e., there exists a constant K > 0 such that (∗) with γs(t) tp instead of s(t) tp is oscillatory for γ > K and nonoscillatory for γ < K.

Introduction to the Galois Theory of Linear Ordinary Differential Equations

We define the differential Galois group of a linear homogeneous ordinary differential equation and illustrate the type of information about solutions packaged within. The initial format is classical; at the end we indicate how the results can be conceptualized geometrically.

The Picard-Vessiot Theory of Homogeneous Linear Ordinary Differential Equations.