序Hilbert空间中的时脉冲中立型泛函微分方程

Impulsive neutral functional differential equations with variable times in ordered Hilbert spaces

研究了时变脉冲中立型泛函微分方程解的存在性,即ddt[y(t)-g(t,y(t))]=f(t,y(t))a.e.t∈J=[0,T];t≠τk(y(t))y(t+)=Ik(y(t))t=τk(y(t));k=1,2,…,my(0)=ξ由于脉冲函数τk(y(t))≠ck,k=1,2,…,m,上述问题通常在有限维空间中有所研究.在此将以往有限维空间中的结论拓展至无穷维的序Hilbert空间,利用Schaefer不动点定理得到了上述问题解的一个存在性定理.对Ik,τk附加一定的条件,保证了由解确定的脉冲函数τk(y(t))最多只与t相交1次.

The impulsive neutral functional differential equation with variable times is studied： {d/dt[y（t）-g（t,y（t））]=f（t,y（t）） a.e.f∈J=[0，T]；t≠Tk（y（t））；y（t^＊）=Ik（y（t） t=Tk（y（t））；k=1,2,…,m；y（0）=ξ Because the moments functions Tk （y （t） ） are unfixed, some research of this problem is usually investigated in finite dimensional spaces. In this paper some conclusions in finite dimensional spaces are extended to infinite dimensional ordered Hilbert spaces by using the Schaefer＇s fixed-point theorem and the existence theorem of solutions for impulsive neutral functional differential equations with variable times is obtained. Some additional conditions are put on Ik，Tk to guarantee that the solution to this problem meets each barrier almost once。