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A nontrivial example of application of the Nielsen fixed-point theory to differential systems: Problem of Jean Leray. (English) Zbl 0964.34030

The Nielsen number is a topological tool which gives a lower estimate on the number of fixed points of a mapping. In this paper, the author searches for a nontrivial application to differential equations. He considers a rather concrete class of periodic differential systems in the plane and concludes, using Nielsen theory, that they have at least three periodic solutions.

MSC:

34C25 Periodic solutions to ordinary differential equations
47H10 Fixed-point theorems
34B15 Nonlinear boundary value problems for ordinary differential equations
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