On Surjective Quadratic Mappings

In the paper, quadratic mappings acting from one finite-dimensional space to another are studied. Sufficient conditions for the stable surjectivity of a quadratic surjective mapping (i.e., for the condition that every quadratic mapping sufficiently close to a given one is also surjective) are obtained. The existence problem for nontrivial zeros of a surjective quadratic mapping acting from $\mathbb{R}^n$ to $\mathbb{R}^n$ is studied. For $n=3$, the absence of these zeros is proved.