Oscillation of linear and half-linear difference equations via modified Riccati transformation

• Autoři: ŠIŠOLÁKOVÁ Jiřina
• Rok publikování: 2023
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Journal of Mathematical Analysis and Applications
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://doi.org/10.1016/j.jmaa.2023.127526
• Doi: http://dx.doi.org/10.1016/j.jmaa.2023.127526
• Klíčová slova: Half-linear equations; Linear equations; Difference equations; Oscillation; Riccati transformation; Riccati equation
• Popis: In this paper, we introduce a new oscillation criterion for Euler type half-linear difference equations with positive coefficients which are asymptotically periodic and bounded, respectively. As the mean of proving the criterion, the generalized adapted Riccati transformation is used. The presented main result is the oscillatory counterpart of a previously obtained non-oscillation criterion for the treated equations. Therefore, the result shows that the analyzed equations are conditionally oscillatory. Then we emphasize the novelty of the result in the linear case by several consequences.

Související projekty

• Diferenciální a diferenční rovnice reálných řádů: kvalitativní analýza a její aplikace