考虑剪切效应弹性板弯曲问题的DQ分析方法

A differential quadrature (DQ) method for orthotropic plates was proposed based on Reddy' s theory of plates with the effects of the higher-order transverse shear deformations. Wang-Bert's DQ approach was also further extended to handle the boundary conditions of plates. The computational convergence was studied, and the numerical results were obtained for different grid spacings and compared with the existing results. The results show that the DQ method is fairly reliable and effective.     

公式法求y″+py′+qy=p_m(x)e~(λx)的特解

求微分方程y″+py′+qy=p_m(x)e~(λx)的特解y~*,传统的方法比较麻烦。本文为此导出求特解y~*之中多项式待定系数的公式,只需简单计算即可求解。     

Decomposition method for solving parabolic equations in finite domains

INTRODUCTION The decomposition method was introduced by Adomian(1989;1994)in the1980’s for solving linear and nonlinear functional equations(algebraic,dif-ferential,partial differential equations(PDEs)and systems,integral,differential-delay,integro-differen-tial equations,etc.)(Adomian,1989;1994;Guellal and Cherruault,1995;Adomian et al.,1996;Laffez and Abbaoui,1996;Ndour et al.,1996;Guellal et al.,1997;Abbaoui and Cherruault,1999;Adjedj,1999).This method leads to computable,accurat…     

求解多项分数阶常微分方程的数值方法

本文考虑多项的分数阶常微分方程。证明了其解的存在性与唯一性;导出了多项的分数阶常微分方程的解;提出了三种数值解法来近似多项的分数阶常微分方程解。第一种方法,利用Diethelm等技巧;第二种方法,利用Caputo分数阶导数,Riemann-Liouville分数阶导数,分数阶导数之间的关系;第三种方法,把多项的分数阶常微分方程转化为分数阶微分方程组,然后利用分数阶预估-校正法。最后给出了一些实际应用例子。     

一阶时滞微分方程临界状态下解的振动性

讨论了在临界状态下一阶时滞微分方程解的振动性 ,获得了使所有解振动的充分条件     

一类二阶非线性方程的Dirichlet边值问题的可解性

考察了一类二阶非线性常微分方程的Dirichlet边值问题的存在性. 在非线性项线性增长的情况下,利用Leray-Schauder不动点定理获得了若干新的存在性结论.     

关于一般微分单项式的值分布(英文)

讨论了一般微分单项式的值分布 ,得到定理 :设 f 是平面上的超越亚纯函数 .F=fn0 (f( i) ) ni… (f( k) ) nk-c,ni≥ 1,c≠ 0是常数 ,那么 (n0 -2 ) T(r,f )≤ N(r,1F ) S(r,f )　 n0 >2T(r,f )≤ 7(i 1)i (Ni) (r,1f ) N(r,1F) ) S(r,f )　 n0 =1T(r,f )≤ 7(N (r,1f ) N(r,1F) ) S(r,f )　 n0 =0 .     

具阻尼项的Klein—Gordon方程组整体解的存在性

讨论了一类具阻尼的Klein-Gordon方程组的初边值问题整体弱解的存在惟一性。     

Existence of positive solutions for fourth order singular differential equations with Sturm-Liouville boundary conditions

By using the upper and lower solutions method and fixed point theory, we investigate a class of fourth - order singular differential equations with the Sturm - Liouville Boundary conditions. Some sufficient conditions are obtained for the existence of C^2 [ 0, 1 ] positive solutions and C^3 [ 0, 1 ] positive solutions.     

Uniqueness of meromorphic functions concerning differential polynomials

Based on a unicity theorem for entire funcitions concerning differential polynomials proposed by M. L. Fang and W. Hong, we studied the uniqueness problem of two meromorphic functions whose differential polynomials share the same 1- point by proving two theorems and their related lemmas. The results extend and improve given by Fang and Hong’s theorem.