What can the zeros of Laplace Transform tell to us?

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Suppose that I have a function $f: \mathbb{R}^+\to \mathbb{R}$ s.t. the LT is $F$.

I'd like to know if there is some solution to $f(x)=0$. I know the solutions of $F(s)=0$. Can I obtain some information for the zeros' existence for $f$?

Thank you.