Oscillation constants for half-linear difference equations with coefficients having mean values

Advances in Difference Equations

Petr Hasil¹  Michal Vesel¹ 

[1] Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic

关键词: half-linear difference equation;    oscillation theory;    conditional oscillation;    oscillation constant;    Euler equation;    Riccati technique;    39A10;    39A21;   

DOI  :  10.1186/s13662-015-0544-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We investigate second order half-linear Euler type difference equations whose coefficients have mean values. We show that these equations are conditionally oscillatory and we explicitly identify the corresponding oscillation constants given by the coefficients. Our results generalize the known ones concerning equations with positive constant, periodic, or (asymptotically) almost periodic coefficients. We also demonstrate the obtained results on examples and we give corollaries. In particular, we get new results even for linear difference equations.

【 授权许可】

CC BY