COMPARISON THEOREMS AND STRONG
OSCILLATION IN THE HALF-LINEAR
DISCRETE OSCILLATION THEORY

PAVEL REHÁK

Abstract:

Consider the second order half-linear difference equation

$${\rm (HL)}\qquad\qquad\triangle(r_k\vert\triangle y_k\vert^{\... ...vert y_{k+1}\vert^{\alpha-1}{\rm sgn}\,y_{k+1}=0,\phantom{XXXX}$$

$$\alpha >1.$$

In the first part we give various types of comparison theorems for this equation, including the so-called telescoping principle, and also for the associated generalized Riccati difference equation. In the second part, we present criteria for strong (non)-oscillation of (HL) and related results. The paper is finished by an example where oscillatory properties of a generalized discrete Euler equation are investigated.