I have a following systeme :

\begin{equation}
\left\{
  \begin{array}{rcr}
    (\beta+\frac{1}{2}\delta^{2})\nu_{1}(u)-\delta\nu_{2}(u)+\nu_{3}(u)& = &0\\
   (\beta+\frac{1}{2}\delta^{2})\upsilon_{1}(u)-\delta\upsilon_{2}(u)+\upsilon_{3}(u)& < &0\\
  \end{array}
\right.
\end{equation}

where


\begin{align*}
&\nu_{1}(u)= q(u)f[q(u)],\\
&\nu_{2}(u)= f[q(u)]^2 + F(x)q(u)f[q(u)],\\
&\nu_{3}(u)= \left(u (f[q(u)])^2 + \frac{1}{2}u^2q(u)f[q(u)]\right),\\
&q[u] := Quantile[NormalDistribution[0, 1], u], \ (the \ quantale \ at \  u)\\
&f[q(u)]=PDF[NormalDistribution[0, 1], q(u)] \ (the \ density \ at \ q(u)),
\end{align*}

and  for the inequality, $\upsilon_{i}(u)=\nu_{i}^\prime(u)$ with respect $q(u)$ for $ i\in \{1,2,3\}$ with $(\beta,\delta,u)\in [0.1]\times[0.1]\times[0.1]$.

I would like to look at the projection of this system of equation onto the plane  $(\beta,\delta)$ and $(u,\delta)$ in Mathematica or in r.

My code sets up the  full 3-d view of the 3D plot, which is not what I want. And I think there are some thing wrong in my picture. I'd like to see two of the views $(\beta,\delta)$ and $(u,\delta)$ on different figure.

    q[u_] := Quantile[NormalDistribution[0, 1], u]
    f[x_] := PDF[NormalDistribution[0, 1], x]
    h1[u_, a_, e_] := ((((a^2)/2 + e)*(-q[u])*(f[q[u]])) - 
    a*(-q[u]*f[q[u]]*u  + f[q[u]]^2) + u*f[q[u]]^2 - 
    (u^2)/2*q[u]*f[q[u]])/(1/6 - a/2 + (a^2)/2 + e)
    h2[u_, a_, e_] := (((a^2)/2 + e)*((q[u]^2) - 1)*f[q[u]]) - 
    a*(u*(q[u]^2 - 1)*f[q[u]] - 3* q[u]*  f[q[u]]^2) + f[q[u]]^3 -
    2*u*q[u]*f[q[u]]^2 - u*q[u]*f[q[u]]^2 + ((u^2)/2)* q[u]^2 - 1)*f[q[u]]
    ContourPlot3D[ h1[u, a, e] == 0, 
    {a, 0, 1}, {u, 0.1, 0.9}, {e, 0, 1.5}, 
    RegionFunction -> Function[{u, a, e}, h2[u, a, e] > 0]]

The graph 3D :
![enter image description here][1]

I want to try do verify if my plot 3D is true and if it is possible to have the projection on both plan $(\beta,\delta)$ and $(u,\delta)$.  

Any thoughts on the best way to do this? 


  [1]: https://i.sstatic.net/iWWIZ.jpg