Topological Methods for Ordinary Differential Equations

The volume contains the texts of four courses, given by
the authors at a summer school that sought to present the
state of the art in the growing field of topological methods
in the theory of o.d.e. (in finite and infinitedimension),
and to provide a forum for discussion of the wide variety of
mathematical tools which are involved. The topics covered
range from the extensions of the Lefschetz fixed point and
the fixed point index on ANR's, to the theory of parity of
one-parameter families of Fredholm operators, and from the
theory of coincidence degree for mappings on Banach spaces
to homotopy methods for continuation principles.
CONTENTS: P. Fitzpatrick: The parity as an invariant for
detecting bifurcation of the zeroes of one parameter
families of nonlinear Fredholm maps.- M. Martelli:
Continuation principles and boundary value problems.- J.
Mawhin: Topological degree and boundary value problems for
nonlinear differential equations.- R.D. Nussbaum: The fixed
point index and fixed point theorems.