Geodesic
On Surjective Quadratic Mappings
Matematičeskie zametki, Tome 99 (2016) no. 2, pp. 181-185

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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.
Keywords: quadratic mapping, quadratic surjective mapping, stable surjectivity. 
@article{MZM_2016_99_2_a2,
     author = {A. V. Arutyunov and S. E. Zhukovskii},
     title = {On {Surjective} {Quadratic} {Mappings}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {181--185},
     publisher = {mathdoc},
     volume = {99},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_2_a2/}
}
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A. V. Arutyunov; S. E. Zhukovskii. On Surjective Quadratic Mappings. Matematičeskie zametki, Tome 99 (2016) no. 2, pp. 181-185. http://geodesic.mathdoc.fr/item/MZM_2016_99_2_a2/