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Fixed points of mappings in Klee admissible spaces

Górniewicz L., Ślosarski M.

Control and Cybernetics

2007

Vol. 36, no 3

825-832

In this paper we generalize the Lefschetz fixed point theorem from the case of metric ANR-s to the case of acceptable subsets of Klee admissible spaces. The results presented in this paper were announced in an earlier publication of the authors.

Once more on the Lefschetz fixed point theorem

Górniewicz L., Ślosarski M.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 2

161-170

An abstract version of the Lefschetz fixed point theorem is presented. Then several generalizations of the classical Lefschetz fixed point theorem are obtained.

Solving equations by topological methods

Górniewicz L.

Opuscula Mathematica

2005

Vol. 25, no. 2

195-225

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 diffrential equations.

Periodic solutions of periodic retarded functional differential equations

Pawłowski M.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 4

353-363

The paper presents a geometric method of finding periodic solutions of retarded functional differential equations (REDE) x'(t) = f(t,x1), where f is T-periodic in t. We construct a pair of subsets of R x R^n called a T-periodic block and compute its Lefschetz number. If it is nonzero, then there exists a T-periodic solution.