Application of Laplace Transform to Circuits containing Diodes, etc
No you cannot, the Laplace transform only applies to linear differential equations. Therefore, in circuit analysis, you can only apply it to linear elements such as Resistors, capacitors and inductors.
However, you can linearize a diode around an operating point &quot;e&quot;, for example
$$ V = V_e + \delta_V \\ $$
$$  I = I_e + \delta_U \\ $$
You will now be able to define a linearized transfer function.
$$ H(s) = \frac{\delta_I}{\delta_V}
 $$
I've used this principle to control in closed-loop the output current of a diode.