Nonoscillation of half‐linear dynamic equations on time scales. (11th March 2021)

• Record Type: Journal Article
• Authors: Hasil, Petr; Kisel'ák, Jozef; Pospíšil, Michal; Veselý, Michal
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 11(2021)
• Page Start: 8775
• Page End: 8797
• Publication Date: 2021-03-11
• Subjects: dynamic equation -- half‐linear equation -- linear equation -- oscillation -- Riccati equation -- time scale; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7304
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.