On surjective quadratic mappings (Q295986)

The authors define a quadratic mapping \(Q:\mathbb{R}^n\to \mathbb{R}^k\) to be stably surjective if there is an \(\varepsilon>0\) such that every quadratic mapping \(\widetilde Q: \mathbb{R}^n\to\mathbb{R}^k\) for which \(\rho(Q,\widetilde Q)<\varepsilon\) is surjective (here \(\rho\) stands for the distance in the space of quadratic mappings). They obtain sufficient conditions for the stable surjectivity of a quadratic surjective mapping. In case \(k=n\), the existence for nontrivial zeros of a surjective quadratic mapping is also studied.