Solution to a nonlinear set of equations

Question

There is a set of $n$ nonlinear equations of the form $f_i(x_1,\dots,x_n)=\gamma_i$ where $x_1,\dots,x_n $ are real non-negative variables, $i\in\{1,\dots,n\},$ and $\gamma_i\in \mathbb R$. The function $f_i$ is increasing in each variable $x_1,\dots,x_n,$ and $f_i=0$ when $x_i=0.$ Is it possible to find a non trivial solution to this set?

Edit:

If this information is not sufficient what are the other features of the functions I should look for?

Answer 1

Possibility of solution: Implicit function theorem. Generally I think you will have to use numerical methods to find an explicit solution