| HASIL, Petr, Jozef KISEL'ÁK, Michal POSPÍŠIL and Michal VESELÝ. Nonoscillation of half-linear dynamic equations on time scales. Mathematical Methods in the Applied Sciences. Wiley, 2021, vol. 44, No 11, p. 8775-8797. ISSN 0170-4214. Available from: https://dx.doi.org/10.1002/mma.7304. |
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@article{1789197,
author = {Hasil, Petr and Kisel'ák, Jozef and Pospíšil, Michal and Veselý, Michal},
article_number = {11},
doi = {http://dx.doi.org/10.1002/mma.7304},
keywords = {dynamic equation; half‐ linear equation; linear equation; oscillation; Riccati equation; time scale},
language = {eng},
issn = {0170-4214},
journal = {Mathematical Methods in the Applied Sciences},
title = {Nonoscillation of half-linear dynamic equations on time scales},
url = {https://doi.org/10.1002/mma.7304},
volume = {44},
year = {2021}
}
TY - JOUR
ID - 1789197
AU - Hasil, Petr - Kisel'ák, Jozef - Pospíšil, Michal - Veselý, Michal
PY - 2021
TI - Nonoscillation of half-linear dynamic equations on time scales
JF - Mathematical Methods in the Applied Sciences
VL - 44
IS - 11
SP - 8775-8797
EP - 8775-8797
PB - Wiley
SN - 01704214
KW - dynamic equation
KW - half‐ linear equation
KW - linear equation
KW - oscillation
KW - Riccati equation
KW - time scale
UR - https://doi.org/10.1002/mma.7304
N2 - The research contained in this paper belongs to the qualitative theory of dynamic equations on time scales. Via the detailed analysis of solutions of the associated Riccati equation and an advanced averaging technique, we provide the description of domain of nonoscillation of very general equations. The results are formulated and proved for half-linear equations (i.e., equations connected to PDEs with one dimensional p-Laplacian) on time scales. Nevertheless, we obtain new results also for linear difference equations. Moreover, the combination of the presented results with previous ones shows that many useful equations are conditionally oscillatory. Such equations are ideal as testing and comparison equations in real-world models which are beyond capabilities of known oscillation and nonoscillation criteria often.
ER -
HASIL, Petr, Jozef KISEL'ÁK, Michal POSPÍŠIL and Michal VESELÝ. Nonoscillation of half-linear dynamic equations on time scales. \textit{Mathematical Methods in the Applied Sciences}. Wiley, 2021, vol.~44, No~11, p.~8775-8797. ISSN~0170-4214. Available from: https://dx.doi.org/10.1002/mma.7304.
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