Differential Eqns: Prove e^mt*x(t)->0 as t->infty for m<1...

purpleswans

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Sep 3, 2008
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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
 
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