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The generalized coincidence index -- application to a boundary value problem

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*Dorota Gabor*

**Address.** Faculty of Mathematics and Computer Science, N. Copernicus
University of Torun, ul. Chopina 12/18, 87-100 Torun, Poland
**E-mail:** dgabor@mat.uni.torun.pl

**Abstract.** In this paper we investigate a general boundary value
problem, which can be rewritten to the coincidence problem of the form
$L(x)= F(x)$, where $L$ is a Fredholm operator of nonnegative index and
$F$ is not necessarily compact map. We apply a homotopy invariant called
a coincidence index.

**AMSclassification.** 34G20, 34B15, 47H09, 55M20

**Keywords.** Fredholm operator, boundary value problem in Banach
space, fixed point index.