I have system of nonlinear equations. Each equation involves algebraic or tanscendental functions (usually step/threshold functions, nothing fancy), but no euqation involves differentials or derivatives. I have problem, that the number of equations are more than number of variables. Can I hope that my system is consistent, can I hope, that it can yield some solution? Is there theory that can answer my question and that can provide easily checkable conditions with whom I can verify wether my system have solutions.
Achh, of course, I can draw 3 hyperboles in 2-dimensional Euclidean space and seek the point that is common to all three curves. Bad luck. But equations involving threshold functions usually have full regions of the plane as the solution and that is why I can hope, that my system can yield solution.
The system of equations
$$e^x=e\\e^x=e$$
has two equations and one variable, and still has one and only one solution, i.e. $x=1$.
Cheating, you say? OK, how about the system of equations
$$e^x=e\\ \sin(\pi x) = 0$$
which also has two equations, one variable and only one solution?