1. Oscillatory properties of second order half-linear difference equations
- Creator:
- Řehák, Pavel
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- half-linear difference equation, Picone identity, Reid Roundabout Theorem, and oscillation criteria
- Language:
- English
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public