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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?

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

triomphe
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  • This is all the information I can derive about the functions for now, because it is a on going research. If it's too broad please specify what sort of information you think will make the problem narrower and better. – triomphe Mar 01 '14 at 13:23

1 Answers1

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

Nox
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