Plot 3d implicit function and inequality

Hi,

I need to plot a 3d equation and inequality, with some constraints. The equation and inequality are the following

(u.^2).*(p.^2).*(1-exp(-r.*z))-2.*u.*p.*t.*(1+exp(-r.*z))+(t.^2).*(1-exp(-r.*z))+4.*exp(-r.*z)=0
and 
(u.^2).*(p.^2).*(1-exp(-r.*z))-2.*u.*p.*t.*(1+exp(-r.*z))+(t.^2).*(1-exp(-r.*z))+4.*exp(-r.*z)<=0

r and t are scalars, say r=0.001 and t=1. u and z can take non-negative values, 0<=u<=1, and 0<=t, while p takes values that either satisfy the equation or inequality. In the case of the equality, I would like to have a 3d plot with u and z in the "lower" axis and p in the "vertical" axis. The same for the inequality though in this case I would need to represent the whole area that satisfies the inequality.

Thanks