【摘要】 给出了二维微分差分方程dxdt =f(x(t - 1) ,y(t- 1) ) ,dydt =g(x ,y ,x(t- 1) ,y(t - 1) )(E)具有周期为 42n +1,42n - 1,42n - 3,… ,47,45 ,43,4的周期解的一个条件 ,并在定理的证明过程中给出了如何求出其相应周期解的方法更多还原

【Abstract】 Using for the most pare geometric methods,many periodic solutions to the two-dimensional differential difference equations are as followsdxdt=f(x(t-1),y(t-1)), dydt=g(x,y,x(t-1),y(t-1)).(E)Authors obtained main results as follows: Let f:R 2R and g:R 4R be real variable function. If there exists a function y=y(x),x∈R,definition the invariane curve of equation (E) by y=y(x).Use y(x),y(x(t-1)) for y,y(t-1) in equation (E).Then equation (E) can be turn into as following from:dxdt=f(x(t-1),y(x(t-1))=defF(x-(t-1)), dydt=f(x,y(x),x(t-1),y(x(t-1)).(E 0)Next let a l be real numbers and l>0.Let F:RR be the l-Periodical bounded function: (ⅰ) F(a)=0, F(x±l)=-F(x),x∈R; (ⅱ) F is uniformly continuons in (a,a+l) and F(y)=F(x)>0,y=2a+l-x,x∈(a,a+l); (ⅲ) 0<d=∫ a+l adxF(x)≤12n+1(n=0,1,2,...). Then the equation (E) has 42n+1,42n-1,...,47,45,43,4-periodic solutions.更多还原