Nonoscillation criteria for damped half-linear dynamic equations with mixed derivatives on a time scale
Nonoscillation criteria for damped half-linear dynamic equations with mixed derivatives on a time scale
复制标题
DOI：
10.1016/j.jmaa.2022.126183
复制
发表时间：
2022-03
影响因子：
1.3
通讯作者：
Kazuki Ishibashi
中科院分区：
文献类型：
--
作者：
Kazuki Ishibashi
在这项研究中，我们研究使用两种类型的阻尼半线性动力方程在一个单一的时间尺度上提供充分条件，以保证非振动的非平凡解的常微分方程和差分方程。如果时标是从所有真实的数或所有自然数的集合中选取的，则这些方程是半线性微分方程和半线性差分方程。作为非振动性定理的一个特点，如果微分方程和差分方程都是线性的，则保证非振动性的条件是相似的。然而，如果两者都是具有一维p-Laplacian的非线性方程，则在非振动条件方面存在差异。一个欧拉型阻尼动力方程作为一个例子，以强调所描述的非振荡条件的相似性和差异。
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-dimensionalp-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.