I'm now solving a system of nonlinear equations (not differential equations). Although I'm able to find a solution for some parameter sets, there are also cases when I can't find a solution. So I'm quite curious about the existence and uniqueness of a system of nonlinear equations. In a lecture note I found it's said a system of $N$ equations with $N$ unknowns in general has a unique solution. But it's just a brief statement, without a reference or proof. So I wonder if there's any such a theorem.
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I bet that lecture note was about linear equations. I mean, look at $x^2=17$. One equation in one unknown, with two solutions. – Gerry Myerson Jul 29 '16 at 08:57
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Surely you are right. So probably I missed something in the lecture note. Thanks! – Pu Zhang Jul 30 '16 at 12:24