purpleswans
New member
- Joined
- Sep 3, 2008
- Messages
- 1
Hi, I have one problem that I am really stuck on, I don't even know where to start it. Here goes:
Given x(t) is a continuous, nonnegative, real valued function on [0,infinity) and for each a>0, there is an L >0 such that x(t) <= L* e^-t +a * the integral (0, t) e^(s-t)*x(s)ds t>=0
Prove that : e^mt * x(t) approaches 0 as t approaches infinity for every m<1
If you can help that would be great!!!
Thanks
Given x(t) is a continuous, nonnegative, real valued function on [0,infinity) and for each a>0, there is an L >0 such that x(t) <= L* e^-t +a * the integral (0, t) e^(s-t)*x(s)ds t>=0
Prove that : e^mt * x(t) approaches 0 as t approaches infinity for every m<1
If you can help that would be great!!!
Thanks