Oscillatory properties of second order half-linear difference equations

Title:

Oscillatory properties of second order half-linear difference equations

Creator:

Řehák, Pavel

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:34f2cbd3-8eeb-4a33-95c3-8d7d58111056
uuid:34f2cbd3-8eeb-4a33-95c3-8d7d58111056

Subject:

half-linear difference equation, Picone identity, Reid Roundabout Theorem, and oscillation criteria

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We study oscillatory properties of the second order half-linear difference equation \[ \Delta (r_k|\Delta y_k|^{\alpha -2}\Delta y_k)-p_k|y_{k+1}|^{\alpha -2}y_{k+1}=0, \quad \alpha >1. \qquad \mathrm{(HL)}\] It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation \[ \Delta (r_k\Delta y_k)-p_ky_{k+1}=0. \] We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

303-321

Source:

Czechoslovak Mathematical Journal | 2001 Volume:51 | Number:2

Harvested from:

CDK

Metadata only:

false