HASIL, Petr, Jozef KISEL'ÁK, Michal POSPÍŠIL a Michal VESELÝ. Nonoscillation of half-linear dynamic equations on time scales. Mathematical Methods in the Applied Sciences. Wiley, 2021, roč. 44, č. 11, s. 8775-8797. ISSN 0170-4214. Dostupné z: 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 a Michal VESELÝ. Nonoscillation of half-linear dynamic equations on time scales. \textit{Mathematical Methods in the Applied Sciences}. Wiley, 2021, roč.~44, č.~11, s.~8775-8797. ISSN~0170-4214. Dostupné z: https://dx.doi.org/10.1002/mma.7304.
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