✦ LIBER ✦
The number of limit cycles in planar systems and generalized Abel equations with monotonous hyperbolicity
✍ Scribed by Antoni Guillamon; Marco Sabatini
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 557 KB
- Volume
- 71
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
✦ Synopsis
We extend some previous results on the maximum number of isolated periodic solutions of generalized Abel equation and rigid systems. The key hypothesis is a monotonicity assumption on any stability operator (for instance, the divergence) along the solutions of a suitable transversal system. In such a case, at most two isolated periodic solutions exist. Under a simple additional assumption, we also prove a uniqueness result for limit cycles of rigid systems. Our results are easily applicable to special classes of equations, since the hypotheses hold when a suitable convexity property is satisfied.