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@article{1483781, author = {Hasil, Petr and Veselý, Michal}, article_location = {Hoboken}, article_number = {6}, doi = {http://dx.doi.org/10.1002/mma.5485}, keywords = {dynamic equation; half-linear equation; linear equation; oscillation criterion; oscillation theory; Riccati technique; timescale}, language = {eng}, issn = {0170-4214}, journal = {Mathematical Methods in the Applied Sciences}, title = {Oscillation result for half-linear dynamic equations on timescales and its consequences}, url = {https://onlinelibrary.wiley.com/doi/full/10.1002/mma.5485}, volume = {42}, year = {2019} }
TY - JOUR ID - 1483781 AU - Hasil, Petr - Veselý, Michal PY - 2019 TI - Oscillation result for half-linear dynamic equations on timescales and its consequences JF - Mathematical Methods in the Applied Sciences VL - 42 IS - 6 SP - 1921-1940 EP - 1921-1940 PB - Wiley SN - 01704214 KW - dynamic equation KW - half-linear equation KW - linear equation KW - oscillation criterion KW - oscillation theory KW - Riccati technique KW - timescale UR - https://onlinelibrary.wiley.com/doi/full/10.1002/mma.5485 L2 - https://onlinelibrary.wiley.com/doi/full/10.1002/mma.5485 N2 - We study oscillatory properties of half-linear dynamic equations on timescales. Via the combination of the Riccati technique and an averaging method, we find the domain of oscillation for many equations. The presented main result is not the conversion of a known result from the theory of differential or difference equations, i.e., we obtain new results for the timescales T = R (for differential equations) and T = Z (for difference equations). Half-linear equations generalize linear equations (in fact, they coincide with certain one-dimensional PDEs with p-Laplacian), but the main result is new also for linear differential and difference equations. The corresponding corollaries and examples are given as well. ER -
HASIL, Petr a Michal VESELÝ. Oscillation result for half-linear dynamic equations on timescales and its consequences. \textit{Mathematical Methods in the Applied Sciences}. Hoboken: Wiley, 2019, roč.~42, č.~6, s.~1921-1940. ISSN~0170-4214. Dostupné z: https://dx.doi.org/10.1002/mma.5485.
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