KdV方程对称李代数的伴随表示及其killing型

本文利用群的开拓理论得出了 Kd V方程对称李代数的伴随表示及其 Killing型 .     

一个不定方程以及它的实数解

研究了一类不定方程 ,并获得了它的所有实数解     

线性泛函方程解的振动性的新结果

本文研究高阶泛函方程x(g(t))=P(t)x(t)+Q1(t)x(g2(t))+…+Qk(t)x(gk+1(t))解的振动性,得到了一些新的振动条件.改进和推广了已有结果.     

R^2上带奇异性的非线性多重调和方程的正整解

该文以Schauder-Tychonoff不动点定理为工具，建立了一类平面上带奇异性的非线性 多重调和方程的正的径向对称整体解的存在性定理，并给出了解的有关性质，所得的结果丰 富和发展文[1][4]的结果。     

广义Benjamin-Bona-Mahony方程Fourier谱方法的大时间误差估计

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅＢｅｎｊａｍｉｎ Ｂｏｎａ Ｍａｈｏｎｙｅｑｕａｔｉｏｎｕｔ+ｕｘ+ｕｕｘ -ｕｘｘ-ｕｘｘｔ =0 ( 1 .1 )ｉｎｃｏｒｐｏｒａｔｅｓｎｏｎｌｉｎｅａｒｄｉｓｐｅｒｓｉｖｅａｎｄｄｉｓｓｉｐａｔｉｖｅｅｆｆｅｃｔｓ ,ａｎｄｈａｓｂｅｅｎｐｒｏｐｏｓｅｄａｓａｍｏｄｅｌｆｏｒｂｏｔｈｔｈｅｂｏｒｅｐｒｏｐａｇａｔｉｏｎａｎｄｔｈｅｗａｔｅｒｗａｖｅｓ[1,2 ] .Ｔｈｅｅｘｉｓｔｅｎｃｅａｎｄｕｎｉｑｕｅｎｅｓｓｏｆｓｏｌｕｔｉｏｎｓｆｏｒｔｈｉｓｅｑｕａｔｉｏｎｈａｖｅｂｅｅ…     

一类时滞Logistic差分方程的全局吸引性

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｎｏｎａｕｔｏｎｏｍｏｕｓｄｅｌａｙｌｏｇｉｓｔｉｃｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎΔｙｎ =ｐｎｙｎ( 1 - ｙτ(ｎ) )　 ,ｎ =0 ,1 ,2 ,...,( 1 1 )ｗｈｅｒｅｐｎ ∞ｎ =0 ｉｓａｓｅｑｕｅｎｃｅｏｆｐｏｓｉｔｉｖｅｒｅａｌｎｕｍｂｅｒｓ ,τ(ｎ) ∞ｎ =0 ｉｓａｎｏｎｄｅｃｒｅａｓｉｎｇｓｅｑｕｅｎｃｅｏｆｉｎｔｅｇｅｒｓ,τ(ｎ) <ｎａｎｄｌｉｍｎ→∞τ(ｎ) =∞ ,Δｙｎ=ｙｎ +1- ｙｎ.Ｍｏｔｉｖａｔｅｄｂｙｐｌａｕｓｉｂｌｅａｐｐｌｉｃａｔｉｏｎｓ…     

一个来自振动理论反问题的矩阵方程

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＲｎ×ｍｄｅｎｏｔｅｔｈｅｒｅａｌｎ×ｍｍａｔｒｉｘｓｐａｃｅ ,Ｒｎ×ｍｒ ｉｔｓｓｕｂｓｅｔｗｈｏｓｅｅｌｅｍｅｎｔｓｈａｖｅｒａｎｋｒ ,ＯＲｎ×ｎｔｈｅｓｅｔｏｆａｌｌｎ×ｎｏｒｔｈｏｇｏｎａｌｍａｔｒｉｃｅｓ,ＳＲｎ×ｎ(ＳＲｎ×ｎ≥ ,ＳＲｎ×ｎ>)ｔｈｅｓｅｔｏｆａｌｌｎ×ｎｒｅａｌｓｙｍｍｅｔｒｉｃ (ｓｙｍｍｅｔｒｉｃｐｏｓｉｔｉｖｅｓｅｍｉｄｅｆｉｎｉｔｅ ,ｐｏｓｉｔｉｖｅｄｅｆｉｎｉｔｅ)ｍａｔｒｉｃｅｓ.ＴｈｅｎｏｔａｔｉｏｎＡ>0 (≥ 0 ,<0 ,≤ 0 )ｍ…     

AD GALERKIN ANALYSIS FOR NONLINEAR PSEUDO—HYPERBOLIC EQUATIONS

AD(Alternating direction)Galerkin schemes for d-dimensional nonlinear pseudo-hyperbolic equations are studied.By using patch approximation technique,AD procedure is realized,and calculation,work is simplified.By using Galerkin approach,highly computational accuracy is kept.By using various priori estimate techniques for differential equations,difficulty coming form non-linearity is treated,and optimal H^1 and L^2 convergence prop-erties are demonstrated.Moreover,although all the existed AD Galerkin schemes using patch approximation are limited to have only one order accuracy in time increment,yet the schemes formulated in this paper have second order accuracy in it.This implies an essential advancement in AD Galerkin aualysis.     

On the United Theory of the Family of Euler-Halley Type Methods with Cubical Convergence in Banach Spaces

The convergence problem of the family of Euler-Halley methods is considered under the Lipschitz condition with the L-average, and a united convergence theory with its applications is presented.     

FRACTIONAL DIFFUSION EQUATIONS WITH INTERNAL DEGREES OF FREEDOM

We present a generalization of the linear one-dimensional diffusion equation by com-bining the fractional derivatives and the internal degrees of freedom. The solutions areconstructed from those of the scalar fractional diffusion equation. We analyze the in-terpolation between the standard diffusion and wave equations defined by the fractionalderivatives. Our main result is that we can define a diffusion process depending on theinternal degrees of freedom associated to the system.