Given, say $4$ non linear equations with $4$ positive parameters,
$f_1(x,y,z,t)=a,\quad f_2(x,y,z,t)=b,\quad f_3(x,y,z,t)=c,\quad f_4(x,y,z,t)=d$
for given $a,b,c,d$, If I am able to show that when the other $3$ variables are fixed, if $f_1$ is increasing with $x$ and $f_2$ is increasing with $y$ and $f_3$ is increasing with $z$ and $f_4$ is increasing with $t$ and all functions have at least a positive point.
Can I claim that this equation system has a unique solution for positive $x,y,z,t$?
Many Thanks.