Boundness And Global Attractability On A Class Of Functional

In the paper, a class of functional differential equation is discussed. Byusing fixed point theory, we obtain some sufficient condition which ensure theboundedness and global attractivity of the system.The main contents in this paper can be summarized as follows.1. Firstly, in the introduction section, we extend a class of scalar functionaldifferential equation to vector form.2. In the third section, we discuss the vector functional differential equationwith bounded delay, x'(t)=A(t)x+d/(dt)integral from n=-L to 0 P(s)integral from n=t+s to t G(x(u))duds (9)By using fixed point theory, we obtain the boundedness and global attractivityof function(9). then, by using theorem 1, we obtain more ordinary result aboutscalar function.3. In the third section, we discuss the vector functional differential equationwith unbounded delay, x'(t)=A(t)x+d/(dt)integral from n=0 to t integral from n=t-s to∞P(v)dvG(x(s))ds (10)By using fixed point theory, we obtain the boundedness and global attractivity offunction (10). Then, by using theorem 2, we obtain more ordinary result aboutscalar function.4. In the third section, we discuss the vector functional differential equationwith infinite delay, x'(t)=A(t)x+d/(dt)integral from n=-∞to t integral from n=-∞to s-t Q(u)duG(x(s))ds (11) By using fixed point theory, we obtain the boundedness and global attractivity offunction (11). Then, by using theorem 3, we obtain more ordinary result aboutscalar function.5. In the third section, we discuss the vector functional differential equationwith pointwise varibale delay, x'(t)=A(t)x-d/(dt)integral from n=h(t) to t B(s)G(x(q(s)))ds (12)By using fixed point theory, we obtain the boundedness and global attractivity offunction (12). Then, by using theorem 3, we obtain more ordinary result aboutscalar function.