函数的振动熵

本文定义了振动函数与函数的振动熵。对函数的振动性质进行了初步的讨论。振动熵是对函数振动程度的度量(振动愈剧烈振动熵的值愈大)。导数是振动熵的特例。     

二阶线性时滞微分方程的广义振动性

本文主要研究了二阶线性时滞微分方程的广义振动性和广义非振动性,给出了方程广义振动和广义非振动的一些判定定理,同时给出了一类方程广义非振动的充要条件.     

高阶线性时滞微分方程的广义振动性

该文考虑了一类高阶线性常系数时滞微分方程 y( n) (t) py′(t) qy(t-τ) =0的广义振动性和广义非振动性 ,给出了一些该类方程广义振动和广义非振动的判定定理 .文中的定理 4还给出了一类非振动但广义振动的方程的判别法则     

一类二阶线性微分方程的振动性及非振动性

本文研究了二阶线性方程的振动性及非振动性问题，建立了若干新的振动与非振动性结果，它们改进并推广了若干已知的定理。     

“一类拟线性二阶微分方程解的振动与非振动的判定”的注记

本文给出了一类拟线性二阶微分方程解振动与非振动的新的判定准则,完善和改进了最近一些文献中的某些结论。     

一类拟线性二阶微分方程解的振动与非振动的判定

本文讨论了拟线性微分方程（ｐ（ｘ＇））＇＋ｑ（ｔ）ｐ（ｘ）＝０,ｔ≥ｔ０,ｑ（ｔ）≥０（这里 ｐ（ｕ）＝｜ｕ｜ｐ－１ｕ,ｐ＞０是常数）的解的振动与非振动条件,并改进了文献［２］的结果．     

厚板振动的三维弹性力学解

本文以弹性动力学的基本方程为基础，推导出厚板的控制方程·给出了在横向强迫力作用下，厚板的应力、位移的动力响应·得出厚板的振动特征是由对称振动、反对称振动和剪切振动的三种模式组成·最后，将简支厚方板作为实例导出自振频率的特征方程，数值计算结果与经典理论、中厚板理论的结果作了比较·     

一类时滞差分方程的振动准则

讨论一类时滞差分方程的振动性,给出了所有解振动的充分条件.     

非线性二阶中立型时滞微分方程的振动和非振动准则

建立了具有正负系数的非线性二阶中立型时滞微分方程(E)的振动和非振动准则,并给出了说明定理应用的例子．所得定理推广和改进了新近文献中的一系列结果．     

脉冲中立型时滞抛物方程的振动性

本文研究了一类脉冲中立型时滞抛物方程解的振动性及强振动性,获得了此类脉冲中立型时滞抛物方程解振动和强振动的代数判据.     

Frequency measures on time scales with applications

The concept of frequency measures of subsets of a time scale is introduced and the relevant properties are discussed. Then, frequent oscillation is defined to strengthen the classical concept of oscillation. Applications are shown by deriving oscillation criteria for first-order dynamic equations on time scales.     

Forced oscillation criteria for superlinear-sublinear elliptic equations via Picone-type inequality

Picone-type inequality is derived for a class of superlinear-sublinear elliptic equations with a forcing term, and oscillation results are established by utilizing the Picone-type inequality. Our approach is to reduce the multi-dimensional oscillation problems to one-dimensional oscillation problems for half-linear ordinary differential equations.     

Oscillations of nonlinear hyperbolic equations with functional arguments via Riccati method

This paper is devoted to the study of the oscillatory behavior of solutions of nonlinear hyperbolic equations with functional arguments by using integral averaging method and a generalized Riccati technique. First, we establish oscillation results for nonlinear hyperbolic equations by applying oscillation criteria for Riccati inequality. Secondly, we present interval oscillation results for nonlinear hyperbolic equations. These results improve and extend oscillation results of Cui and Xu [1].     

On oscillation of nonlinear second-order differential equations with damping term

The paper is concerned with oscillation of a novel class of nonlinear differential equations with a damping term. First it is demonstrated how known oscillation results for another intensively studied class of equations can be translated to the one in question, and vice versa. Advantages and drawbacks of such translation are carefully examined. Then an oscillation criterion for the new class of equations is established. The principal result of the paper is compared to those reported in the literature, and an illustrative example to which known oscillation criteria fail to apply is provided.     

Oscillation behavior of solution of impulsive fractional differential equation

In this paper, we study the oscillation of impulsive Caputo fractional differential equation. Sufficient conditions for the asymptotic and oscillation of the equation are obtained by using the inequality principle and Bihari Lemma. An example is given to illustrate the results. This is the first time to study the oscillation of impulsive fractional differential equation with Caputo derivative.     

Non-linear oscillation of the fluid in a plate capacitor

Employing the principle of virtual work the equation of motion for the liquid between two electrode walls of a charged parallel plate capacitor is established. Analysis in phase plane stands out the motion is non-linear oscillation. The phase orbit is determined then the oscillation period is expressed with elliptic integrations. Besides the intrinsic parameters in the system, the initial disturbing conditions affect the oscillation period, which readily demonstrates the non-linearity of oscillation. The characters of the period are discussed and the approximate computation is presented. Further, the threshold of control voltage under which the results can be still used for the capacitor with an inclined plate is achieved.     

Oscillation criteria for boundary value problems of high-order partial functional differential equations

In this paper, a class of boundary value problems associated with high-order partial functional differential equations with distributed deviating arguments is investigated. Some oscillation criteria of solutions to the problem are developed. Our approach is to reduce the multi-dimensional oscillation problem to a one-dimensional oscillation one by employing some integral means of solutions and introducing some parameter functions. One illustrative example is considered.     

Numerical approach for solving fractional relaxation–oscillation equation

In this study, we will obtain the approximate solutions of relaxation–oscillation equation by developing the Taylor matrix method. A relaxation oscillator is a kind of oscillator based on a behavior of physical system’s return to equilibrium after being disturbed. The relaxation–oscillation equation is the primary equation of relaxation and oscillation processes. The relaxation–oscillation equation is a fractional differential equation with initial conditions. For this propose, generalized Taylor matrix method is introduced. This method is based on first taking the truncated fractional Taylor expansions of the functions in the relaxation–oscillation equation and then substituting their matrix forms into the equation. Hence, the result matrix equation can be solved and the unknown fractional Taylor coefficients can be found approximately. The reliability and efficiency of the proposed approach are demonstrated in the numerical examples with aid of symbolic algebra program, Maple.     

Modelling non-Fourier heat conduction with periodic thermal oscillation using the finite integral transform

The non-Fourier heat conduction in a finite medium subjected to a periodic heat flux is modelled using the finite integral transform technique and an analytic solution is obtained. An analogy between thermal oscillation and oscillation of mechanical and electrical systems is drawn. A transition criterion from the non-Fourier heat conduction formulation to the Fourier formulation is obtained and a simple analytical expression of the phase and amplitude of thermal oscillation is derived.     

Oscillation of even order partial differential equations with distributed deviating arguments

Some Kamenev-type oscillation criteria are established for a class of boundary value problems associated with even-order partial differential equations with distributed deviating arguments. Our approach is to reduce the high-dimensional oscillation problem to a one-dimensional oscillation one, and the general means developed by Philos and Wong is used as the main tool. The results obtained here extend and improve some known results in the literature.