11 citations · 15 across the 17 of their papers we have counts for
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A variational approach to Hilbert's 16th problem within the framework of global analysis
Pablo Pedregal
We focus on the second part of Hilbert's 16th problem and provide an upper bound on the number of limit cycles that a polynomial, differential, planar system may have, depending ex…
Hilbert's 16th problem. II. Pfaffian equations and variational methods
Pablo Pedregal
Starting from a Pfaffian equation in dimension and focusing on compact solutions for it, we place in perspective the variational method used in [29] to solve Hilbert's 16th pro…
Hilbert's 16th problem. I. When differential systems meet variational methods
Jaume Llibre, Pablo Pedregal
We provide an upper bound for the number of limit cycles that planar polynomial differential systems of a given degree may have. The bound turns out to be a polynomial of degree fo…
Hilbert's 16th problem. When variational principles meet differential systems
Jaume Llibre, Pablo Pedregal
Thanks to the interest of many people, a mistake has been found in our way of counting limit cycles. We are working on a new version.