Does laplace transform of $y(x)^2$ exists?

Question

Suppose laplacian of $y(x)$ is $Y(s)$. Then what will be the laplacian of $y(x)^2$. Does it even exists?

Answer 1

There is no "rule" for that, only in some special cases, for example $y(x)=x^n$ or $y(x)=c$ or $y(x)=e^{ax}$.