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Qualitative Behavior for Fourth-Order Nonlinear Differential Equations

机译：四阶非线性微分方程的定性行为

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In this paper, new an oscillation criterion for a class of fourth-order nonlinear delay differential equations are established by using the double generalized Riccatti substitutions. Recently, there has been increasing interest related to the theory of delay differential equations (DDEs), this has been attributed to the important of understanding of application in delay differential equations. Recent applications that include delay differential equations continue to appear with increasing frequency in the modeling of diverse phenomena in physics, biology, ecology, and physiology. So, other authors have been attracted to finding the solutions of the differential equations or deducing important characteristics of them has received the attention of many authors. The solution to this equation is important in order to understand these issues and phenomena, or at least to know the characteristics of the solutions to these equations. But, differential equations such as those used to solve real life problems may not necessarily be directly solvable, i.e., do not have closed form solutions. The main objective of this work is to provide an opportunity to study the new trends and analytical insights of the delay differential equations, existence and uniqueness of the solutions, boundedness and persistence, oscillatory behavior of the solutions, stability and bifurcation analysis, parameter estimations and sensitivity analysis, and numerical investigations of solutions. One objective of our paper is to further simplify and complement some well-known results which were published recently in the literature. An illustrative example is included.
机译：本文利用双重广义Riccatti替换建立了一类四阶非线性时滞微分方程的振动准则。近来，与延迟微分方程（DDE）理论相关的兴趣日益增加，这归因于理解在延迟微分方程中的应用的重要性。在物理，生物学，生态学和生理学中的各种现象的建模中，包括延迟微分方程在内的最新应用继续以越来越高的频率出现。因此，吸引了其他作者来寻找微分方程的解或推导它们的重要特性受到了许多作者的关注。为了理解这些问题和现象，或者至少了解这些方程的解的特征，该方程的解很重要。但是，诸如用于解决现实生活中的问题的微分方程可能不一定可以直接求解，即没有封闭形式的解。这项工作的主要目的是提供一个机会，研究延迟微分方程的新趋势和分析见解，解的存在与唯一性，解的有界性和持久性，解的振荡行为，稳定性和分叉分析，参数估计和敏感性分析和解决方案的数值研究。本文的一个目标是进一步简化和补充最近在文献中发表的一些著名结果。包括说明性示例。

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