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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.

Some remarks about a generalized method of summability of series

Herzog M.

Fasciculi Mathematici

1999

Nr 30

57-61

In this paper we investigate certain methods of summability of series. We obtain a conection between those methods.

Some properties of solutions of singular equation

Herzog M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1998

[Z] 38

37-42

In this note we give a theorem on the behaviour of solutions of a singular differential equation at singular points.