Non-oscillation criterion for generalized Mathieu-type differential equations with bounded coefficients
Non-oscillation criterion for generalized Mathieu-type differential equations with bounded coefficients
复制标题
有界系数广义Mathieu型微分方程的不振荡判据
DOI：
10.1090/proc/15626
复制
发表时间：
2022
影响因子：
1
通讯作者：
Ishibashi Kazuki
中科院分区：
文献类型：
--
作者：
Ishibashi Kazuki;Ishibashi Kazuki;Ishibashi Kazuki;Jitsuro Sugie and Kazuki Ishibashi;Ishibashi Kazuki
本文考虑以下方程：\开始{方程 *} x“+（-\alpha+\beta\cos（\rho t）+ f（t））x= 0，\结束{方程 *}其中参数和是真实的数，频率是正的真实的数，是一个连续有界函数，即存在一个正的常数使得对于。这个方程通常被称为Mathieu方程。这项工作提出了一个非振荡定理，可以应用，即使。所需条件由参数、、和正常数表示。本文获得的结果包括Sugie和Ishibashi的结果[Appl. Math. Comput. 346（2019），pp. 491-499]。此外，可以使用Sugie [Monatsh.]提出的相平面分析来证明该结果。186（2018），pp. 721-743]。最后，总结了广义Mathieu方程的简单非振动性和振动性条件。引用
The following equation is considered in this work:\begin {equation*} x''+(-\alpha+\beta\cos (\rho t)+ f (t)) x= 0,\end {equation*} where the parametersandare real numbers, the frequencyis a positive real number, andis a continuous bounded function, ie, there exists a positive constantsuch thatfor. This equation is generally referred to as the Mathieu equation when. This work proposes a non-oscillation theorem that can be applied even if. The required conditions are expressed by the parameters,,, and a positive constant. The results obtained herein include those by Sugie and Ishibashi [Appl. Math. Comput. 346 (2019), pp. 491–499]. Further, the result can be proved using the phase plane analysis proposed by Sugie [Monatsh. Math. 186 (2018), pp. 721–743]. Finally, the simple non-oscillation and oscillation conditions of the generalized Mathieu equation are summarized. References