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Solving a convolution equation: two solutions, which one is correct?

Hi All,

Here is my problem:

Considering the following equation,

Ur(t)*G(t)=A

- Ur(t) is what we are looking for and is =0 for all t<0

- * is a convolution

- G(t) = 1/Q1 + (P1/Q2-1/Q1)exp(-Q1.t/Q2) for t>=0 (Q1, Q2 and P1 are constants) and G(t)=0 for all t<0

- A is a constant

I derived a solution using the Laplace Transform and also found a way to get a solution through a derivation in the time domain using the Stieltjes integrals . Both derivations are in the .doc attached

The issue is that the two solutions are different and I don't know why...

Which one is correct if any?(Wondering)

Thanks for your help or ideas,

MatNorge