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In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.

The Lefschetz and the Nielsen periodic point theorems are developed for compact absorbing contractions on ANRs. These results are reformulated in terms of discrete multivalued semi-dynamical systems. They are also applied to Carathe´odory differential inclusions on tori for obtaining the existence and multiplicity results for boundary value problems. [Copyright &y& Elsevier]