变系数波方程振动传递的边界镇定

本文讨论了变系数波方程振动传递的边界镇定,应用黎曼几何方法和迹的正则性得到了所讨论问题的能量一致衰减率.     

带有时滞边界反馈的退化波动方程的镇定

该文在一维空间中研究了带有时滞边界反馈的退化波动方程的镇定问题.首先运用半群理论证明了其解的适定性,然后通过选用合适的乘子以及构造合适的Lyapunov泛函,证明了该退化波动方程解的指数稳定性结果.     

变系数波动方程的边界镇定

应用Riemann几何方法和乘子方法,得到一定条件下变系数波动方程在线性边界反馈下能量的指数衰减性.     

波方程的边界镇定性的分析(英文)

利用乘子法研究了带有变系数的波方程的反馈镇定问题．文章中变系数ｑ（ｘ）分为两种情况：（Ｈ_１）ｑ和（Ｈ_２）ｑ．同时还引入了敏感反馈系数和波方程能量的指数衰减域．更为重要的是,本文统一和改善了一些以前已有的结果．     

高阶变系数函数方程的非振动解

给出一类高阶非线性函数方程的一些新的非振动准则,并且给出了在差分方程中的若干应用,结果改进和推广了近期文献的某些结果.     

高阶变系数函数方程的振动性

建立了一类高阶非线性变系数函数方程一切解振动的几个充分条件,并且给出了在差分方程中的若干应用.结果全面推广了某些文献的结果.     

变系数浅水波方程的精确解

均衡作用法给出了一种求非线性发展方程孤波解的有效方法.利用该方法,运用计算机符号计算,求出了变系数的一般浅水波方程的孤子解.     

具有连续变量的变系数差分方程的振动性

本文建立了具有连续交量的变系数差分方程振动的充分条件，改进了最近文献中的一些结果．     

具有变系数的二阶中立型差分方程的有界振动

研究一类具有连续变量的二阶中立型时滞差分方程，给出了该类方程一切有界解振动的几个充分条件.     

一类非线性变系数差分方程正解的振动性

研究了一类具有时滞的非线笥变系数差分方程Ｘｎ＋１＝Ｘｎｅｘｐ（ｒｎ１－ｘｎ－ｋ／１－ｃｘｎ－ｋ解的振动性,获得了其正解关于正平衡点ｘ＝１振动的好的充分条件。     

NONLINEAR BOUNDARY STABILIZATION OF WAVE EQUATIONS WITH VARIABLE COEFFICIENTS

The wave equation with variable coefficients with a nonlinear dissipative boundary feedback is studied. By the Riemannian geometry method and the multiplier technique, it is shown that the closed loop system decays exponentially or asymptotically, and hence the relation between the decay rate of the system energy and the nonlinearity behavior of the feedback function is established.     

变系数函数方程解的振动准则

本文建立了一类变系数非线性函数方程一切解振动的几个充分条件,并且给出了它们在差分方程中的若干应用。本文的结果改进和推广了近期文献的某些结果。     

OSCILLATION OF ADVANCED DIFFERENCE EQUATIONS WITH VARIABLE COEFFICIENTS

The oscillations of the advanced difference equationsxn - xn-1 - p(n)xn+k = 0, n ≥ 0, (*)andXn - Xn-1 - ∑i=1mpi(n)xn+ki=0, n ≥0, (**)are investigated, where p(n),pi(n)(i = 1,2,..., m) are nonnegative real numbers. First. a sufficienet condition for the oscillation of equation (*) is obtained, then the result is generalized to the equation (**). At last, an example is given to illustrate the advantages of our results. Our results are new.     

变系数函数方程解的振动性

本文给出了变系数函数方程ｘ（ｇ（ｔ））＝Ｐ（ｔ）ｘ（ｔ）＋∑Ｑｉ（ｔ）ｘ（ｇｋ＋ｉ（ｔ））的一切解均ｉ＝１为振动的充分条件,其中Ｋ≥１为正整数．     

THE SOLUTION OF THE CAUCHY PROBLEM FOR A WAVE EQUATION WITH VARIABLE COEFFICIENTS

Let \[{\mathfrak{M}_k}\] denote the space of Lorentz witb. constant curvature: \[1 + {K_{\eta pq}}{x^p}{x^q}\] where K is a constant and \[\eta = ({\eta _{pq}})\]=diag [1,... 1,-1], We have considered the wave equation with variable coefficients \[\frac{\partial }{{\partial {x^j}}}(\sqrt {|\tilde g|} ){{\tilde g}^{jk}}\frac{{\partial u}}{{\partial {x^k}}}) = 0\] in \[{\mathfrak{M}_k}\] where \[|\tilde g| = |1 + {K_{\eta pq}}{x^p}{x^q}{|^{ - (n + 1)}},{{\tilde g}^{jk}} = (1 + {K_{\eta pq}}{x^p}{x^q})({\eta _{jk}} + K{x^j}{x^k})\] and found the explicit solution of the Cauchy problem for equation (1)     

具有无界时滞的变系数差分方程解的振动性

本文对一类具有无界时滞的变系数差分方程的解的振动性建立了几个新的准则,　推广了［６］的结论．     

ON THE NONLINEAR BOUNDARY STABILIZATION OF THE WAVE EQUATION

The author studies the energy decay rate for the wave equation in a bounded domain under-weak growth assumptions on the feedback function and, applying an integral inequality well adapted to this type of problems, improves some earlier results of Zuazua and of Rao ans Conrad.     

变系数二元线性差分方程解的显式表示

文章讨论了变系数二元线差分方程求解公式,并给出两个应用实例。     

GENERAL DECAY OF A TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATIONS WITH BOUNDARY MEMORY CONDITION

In this paper, we investigate the influence of boundary dissipation on the de-cay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of relaxation function.