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.     

二阶变时滞时标动力系统的振动准则

利用广义Riccati变换及完全平方技巧,讨论了一类时标上的二阶非线性变时滞动力系统的振动性,获得了新的振动准则.     

时标上的二阶变时滞动力方程的振动准则

利用广义Riccati技巧及完全平方技巧,讨论了一类时标上的二阶非线性变时滞动力方程的振动性,得到了一些新的振动准则.     

具有振动系数时滞差分方程解的振动性

本文研究了一类具振动系数时滞差分方程解的振动性,给出了一个新的振动准则,改进了已有文献中许多相关的结果．     

二阶强次线性泛函微分方程解的振动性质

讨论了一类二阶强次线性泛函微分方程解的振动性质,获得了三个新的振动性定理,推广和改进了Grace和Lalli(J.Math.Anal.Appl,1987,123,584—588)的结果.     

Oscillation results for fourth-order nonlinear dynamic equations

This work is concerned with the oscillation of a certain class of fourth-order nonlinear dynamic equations on time scales. A new oscillation result and an example are included.     

一类二阶非线性阻尼微分方程解的振动性质

研究了一类二阶非线性阻尼微分方程解的振动性质.在一定条件下,建立了四个新的振动性定理,推广和改进了已知的结果.     

二阶非线性摄动微分方程解的振动性质

研究了一类二阶非线性摄动微分方程解的振动性质.在一定条件下,建立了两个新的振动性定理,推广和改进了已知的结果.     

二阶非线性阻尼微分不等式解的振动性质

研究了一类二阶非线性阻尼微分不等式解的振动性质.在一定条件下,建立了两个新的振动性定理,推广和改进了已知的结果.     

一类二阶半线性时滞微分方程解的振动性质

研究了一类二阶半线性时滞微分方程解的振动性质.在一定条件下,建立了两个新的振动性定理,推广和改进了已知的结果.     

OSCILLATION OF A SECOND-ORDER HALF-LINEAR NEUTRAL DAMPED DIFFERENTIAL EQUATION WITH TIME-DELAY

In this paper,the oscillation for a class of second-order half-linear neutral damped differential equation with time-delay is studied.By means of Yang-inequality,the generalized Riccati transformation and a certain function,some new sufficient conditions for the oscillation are given for all solutions to the equation.     

Oscillation of second-order nonlinear differential equations with nonlinear damping

This paper is concerned with the oscillation of a class of general type second-order differential equations with nonlinear damping terms. Several new oscillation criteria are established for such a class of differential equations under quite general assumptions. Examples are also given to illustrate the results.     

一类二阶非线性泛函微分方程的振动性定理

研究了一类较为广泛的二阶非线性泛函微分方程解的振动性质.在一定条件下,利用广义黎卡提变换、积分平均技巧和分类讨论的方法建立了两个新的振动准则,改进和推广了已知的一些结果.     

OSCILLATION RESULTS FOR A SECOND ORDER NEUTRAL DELAY DIFFERENTIAL EQUATIONS

Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The relevance of our theorems is illustrated with two carefully selected examples.     

Oscillation of linear Hamiltonian systems

We establish new oscillation criteria for linear Hamiltonian systems using monotone functionals on a suitable matrix space. In doing so we develop new criteria for oscillation involving general monotone functionals instead of the usual largest eigenvalue. Our results are new even in the particular case of self-adjoint second order differential systems.

     

一类二阶非线性泛函微分方程的振动性质

研究了一类较为广泛的二阶非线性泛函微分方程解的振动性质.在一定条件下,利用广义黎卡提变换和积分平均技巧建立了方程(1)的两个新的振动准则,推广和改进了已知的一些结果.     

Oscillation criteria for second-order nonlinear differential equations with damping

For a second-order nonlinear differential equation with a damping term, we obtain new oscillation criteria without an assumption that has been required for related results reported in the literature over the last two decades. Two approaches refining the standard integral averaging technique suggested in the paper can be used to derive a variety of simpler oscillation theorems for different classes of nonlinear differential equations, and both sets of oscillation criteria established in the paper are of independent interest. Several examples are provided to illustrate the relevance of the new theorems.     

Oscillation criteria for certain third-order variable delay functional dynamic equations on time scales

The oscillation of certain third-order nonlinear variable delay functional dynamic equations with nonlinear neutral on time scales is discussed in this article. By using the generalized Riccati transformation and a lot of inequality techniques, some new oscillation criteria for the equations are established. Many of the results are new for the corresponding third-order difference equations and differential equations are as special cases. Some examples are given to illustrate the importance of our results.     

Oscillation of the half-linear PDE in general exterior domains—the variational approach

In the paper a variational technique is used to show how to derive new oscillation criteria for the half-linear partial differential equation via the oscillation criteria for the ordinary half-linear differential equation. In contrast to the results usually found in the literature, general types of unbounded domains can be considered.     

Free and forced finite amplitude oscillation of a spherical shell of radially isotropic elastic material

A spherical elastic shell with radial transverse isotropy is considered. The periods of finite amplitude radial oscillation of the shell have been obtained in two cases, namely (i) when both the surfaces of the shell are free from traction, and (ii) when the shell boundaries are uniformly loaded in such a way that the pressure difference between inner and outer surfaces is constant with respect to time. It is observed that for free oscillation to take place it is necessary to impose a new restriction on the strain energy function in addition to those already obtained for finite amplitude oscillation of an isotropic elastic shell. In the forced oscillation case however the required conditions are of the same form as in the corresponding case for isotropic media.