The oscillation of a delay difference equationis studied and the necessary and sufficient condition for all positive solutions of (E) to oscillate about its positive equilibrium is obtained.
An oscillation criterion is obtained for even order neutral type difference equations of the following formwhere m > 2 is even, no is a nonnegative integer, A is the forward difference operator defined by zn =xn+1 ...An oscillation criterion is obtained for even order neutral type difference equations of the following formwhere m > 2 is even, no is a nonnegative integer, A is the forward difference operator defined by zn =xn+1 - xn,and for i >1, i is the ith-order forward difference operator defined by ixn = A(i-1xn), r and o are positive integers.展开更多
By using the concept of almost periodic 'sequence', that is, a real valued function on Z satisfying the Bohr almost periodic condition, sufficient conditions are obtained for the existence of almost periodic s...By using the concept of almost periodic 'sequence', that is, a real valued function on Z satisfying the Bohr almost periodic condition, sufficient conditions are obtained for the existence of almost periodic solutions of Lasota-Wazewska-type differential equations with almost periodic time dependence.展开更多
Some nonclassical potential symmetry generators and group-invariant solutions of heat equation and wave equation were determined. It is shown that some new explicit solutions of partial differential equations in conse...Some nonclassical potential symmetry generators and group-invariant solutions of heat equation and wave equation were determined. It is shown that some new explicit solutions of partial differential equations in conserved form can he constructed by using the nonclassical potential symmetry generators which are derived from their adjoint system. These explicit solutions cannot he obtained by using the Lie or Lie-Baeicklund symmetry group generators of differential equations.展开更多
文摘本文利用一种新方法对Fokker- Planck方程的非古典势对称群生成元进行研究,找到方程的几个非古典势对称群生成元,并采用非古典对称群方法由这些对称群生成元构造得到Fokker- Planck方程的相应显式解.这些新显式解不能由Fokker -Planck方程本身的Lie对称或Li-e B cklund对称来获得.在验证所求得显式解的过程中,还发现并得到了另外几个显式解.这些新显式解则不能由Fokker -Planck方程本身的Lie对称,Lie- B cklund对称或非古典势对称来获得.文章表明,通过偏微分方程的非古典势对称群生成元来寻找其显式解是可能的.
基金This work is supported by National Natural Sciences Foundation of China.
文摘The oscillation of a delay difference equationis studied and the necessary and sufficient condition for all positive solutions of (E) to oscillate about its positive equilibrium is obtained.
基金This work is supported by National Natural Sciences Foundation of People's Republic of China under Grant 10061004 and Natural Sciences Foundation of Yunnan Province
文摘An oscillation criterion is obtained for even order neutral type difference equations of the following formwhere m > 2 is even, no is a nonnegative integer, A is the forward difference operator defined by zn =xn+1 - xn,and for i >1, i is the ith-order forward difference operator defined by ixn = A(i-1xn), r and o are positive integers.
基金This work is partially supported by the Natural Sciences Foundation of P.R.China under Grant10061004the ABRF of Yunnan Province, P.R.China.
文摘By using the concept of almost periodic 'sequence', that is, a real valued function on Z satisfying the Bohr almost periodic condition, sufficient conditions are obtained for the existence of almost periodic solutions of Lasota-Wazewska-type differential equations with almost periodic time dependence.
基金Project supported by the National Natural Sciences Foundation of China (No.10272021) and the Doctoral Program Foundation of Education Ministry of China (No.20040007022)
文摘Some nonclassical potential symmetry generators and group-invariant solutions of heat equation and wave equation were determined. It is shown that some new explicit solutions of partial differential equations in conserved form can he constructed by using the nonclassical potential symmetry generators which are derived from their adjoint system. These explicit solutions cannot he obtained by using the Lie or Lie-Baeicklund symmetry group generators of differential equations.
