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.


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