Oscillation result for half‐linear dynamic equations on timescales and its consequences. (17th January 2019)

• Record Type: Journal Article
• Authors: Hasil, Petr; Veselý, Michal
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 6(2019)
• Page Start: 1921
• Page End: 1940
• Publication Date: 2019-01-17
• Subjects: dynamic equation -- half‐linear equation -- linear equation -- oscillation criterion -- oscillation theory -- Riccati technique -- timescale; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5485
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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, ie, 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.