Nonoscillation criteria for damped half-linear dynamic equations with mixed derivatives on a time scale

• Published in: Journal of mathematical analysis and applications Vol. 512; no. 2; p. 126183
• Main Author: Ishibashi, Kazuki
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.08.2022
• Subjects: Half-linear dynamic equations; Mixed derivatives; Nonoscillation; Riccati dynamic equations; Time scale; Riccati dynamic equations; Mixed derivatives; Half-linear dynamic equations; Time scale; Nonoscillation
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2022.126183

In this study, we investigate the use of two types of damped half-linear dynamic equations on a single time scale to provide sufficient conditions to guarantee nonoscillation for nontrivial solutions of both ordinary differential equations and difference equations. If the time scale is selected from the sets of all real numbers or all natural numbers, then these equations are half-linear differential and half-linear difference equations. As a feature of the nonoscillation theorems provided, if both the differential and difference equations are linear, the conditions ensuring nonoscillation are similar. However, if both are nonlinear equations with a one-dimensional p-Laplacian, differences exist in the nonoscillatory conditions. An Euler-type dynamic equation with damping is presented as an example to emphasize the similarities and differences in the nonoscillatory conditions described.