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Implicit Mapping Theorem for Singular Points

Fijałkowski P.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2003

Vol. 51, nr 4

445-455

This paper deals with an implicit mapping defined by zeros of a differentiable mapping in a neighbourhood of a singular point, in which a number of partial deratives with respect to the range space of an implicit function vanishes. The main theorem is applied to the bifurcation theory, particularly to a certain version of the Lyapunov-Schmidt reduction.