Differential inequality and non-oscillation of fourth order differential equation

The oscillatory theory of fourth order differential equations has not yet been developed well enough. The results are known only for the case when the coefficients of differential equations are power functions. This fact can be explained by the absence of simple effective methods for studying such higher order equations. In this paper, the authors investigate the oscillatory properties of a class of fourth order differential equations by the variational method. The presented variational method allows to consider any arbitrary functions as coefficients, and our main results depend on their boundary behavior in neighborhoods of zero and infinity. Moreover, this variational method is based on the validity of a certain weighted differential inequality of Hardy type, which is of independent interest. The authors of the article also find two-sided estimates of the least constant for this inequality, which are especially important for their applications to the main results on the oscillatory properties of these differential equations.

Asymptotic and Oscillatory Properties of Noncanonical Delay Differential Equations

In this work, by establishing new asymptotic properties of non-oscillatory solutions of the even-order delay differential equation, we obtain new criteria for oscillation. The new criteria provide better results when determining the values of coefficients that correspond to oscillatory solutions. To explain the significance of our results, we apply them to delay differential equation of Euler-type.

Weighted differential inequality and oscillatory properties of fourth order differential equations

In this paper, we investigate the oscillatory properties of two fourth order differential equations in dependence on boundary behavior of its coefficients at infinity. These properties are established based on two-sided estimates of the least constant of a certain weighted differential inequality.

New Criteria for Oscillation of Half-Linear Differential Equations with p-Laplacian-Like Operators

In this paper, new oscillatory properties for fourth-order delay differential equations with p-Laplacian-like operators are established, using the Riccati transformation and comparison method. Moreover, our results are an extension and complement to previous results in the literature. We provide some examples to examine the applicability of our results.

Oscillatory Behavior of Second-Order Neutral Differential Equations

In this paper, we study oscillatory properties of neutral differential equations. Moreover, we discuss some examples that show the effectiveness and the feasibility of the main results.

Enlightenment on oscillatory properties of 23 class B notifiable infectious diseases in the mainland of China from 2004 to 2020

A variety of infectious diseases occur in mainland China every year. Cyclic oscillation is a widespread attribute of most viral human infections. Understanding the outbreak cycle of infectious diseases can be conducive for public health management and disease surveillance. In this study, we collected time-series data for 23 class B notifiable infectious diseases from 2004 to 2020 using public datasets from the National Health Commission of China. Oscillatory properties were explored using power spectrum analysis. We found that the 23 class B diseases from the dataset have obvious oscillatory patterns (seasonal or sporadic), which could be divided into three categories according to their oscillatory power in different frequencies each year. These diseases were found to have different preferred outbreak months and infection selectivity. Diseases that break out in autumn and winter are more selective. Furthermore, we calculated the oscillation power and the average number of infected cases of all 23 diseases in the first eight years (2004 to 2012) and the next eight years (2012 to 2020) since the update of the surveillance system. A strong positive correlation was found between the change of oscillation power and the change in the number of infected cases, which was consistent with the simulation results using a conceptual hybrid model. The establishment of reliable and effective analytical methods contributes to a better understanding of infectious diseases’ oscillation cycle characteristics. Our research has certain guiding significance for the effective prevention and control of class B infectious diseases.

On the Oscillatory Properties of Solutions of Second-Order Damped Delay Differential Equations

In the work, a new oscillation condition was created for second-order damped delay differential equations with a non-canonical operator. The new criterion is of an iterative nature which helps to apply it even when the previous relevant results fail to apply. An example is presented in order to illustrate the significance of the results.

On the Oscillation Criteria for Fourth-Order p -Laplacian Differential Equations with Middle Term

In this paper, we study the oscillatory properties of the solutions of a class of fourth-order p -Laplacian differential equations with middle term. The new oscillation criteria obtained by using the theory of comparison with first- and second-order differential equations and a refinement of the Riccati transformations. The results in this paper improve and generalize the corresponding results in the literatures. Three examples are provided to illustrate our results.

Symmetry and Its Importance in the Oscillation of Solutions of Differential Equations

Oscillation and symmetry play an important role in many applications such as engineering, physics, medicine, and vibration in flight. The purpose of this article is to explore the oscillation of fourth-order differential equations with delay arguments. New Kamenev-type oscillatory properties are established, which are based on a suitable Riccati method to reduce the main equation into a first-order inequality. Our new results extend and simplify existing results in the previous studies. Examples are presented in order to clarify the main results.

Emden–Fowler-type neutral differential equations: oscillatory properties of solutions

In this paper, we study the oscillation of a class of fourth-order Emden–Fowler delay differential equations with neutral term. Using the Riccati transformation and comparison method, we establish several new oscillation conditions. These new conditions complement a number of results in the literature. We give examples to illustrate our main results.