Coexistence of subharmonic periodic solutions having various periods of differential inclusions on the circle with admissible impulses of degrees \(D=-1,0,1\). (English) Zbl 1454.37039
Summary: Our new Sharkovsky-type cycle coexistence theorems for multivalued admissible maps on the circle, whose degrees equal \(d=-1,0,1\), are derived and applied to impulsive differential inclusions. Although the obtained theorems for admissible maps of degrees \(d=-1,0\) can be formulated “only” in terms of irreducible periodic orbits of coincidences, they are sufficient for effective applications. The most delicate case for \(d=1\) demands a different approach, because the maps can be fixed point free. On the other hand, unlike for degrees \(d=-1,0\), the results for admissible maps of degree 1 can be also exclusively applied to differential inclusions without impulses.
MSC:
| 37E10 | Dynamical systems involving maps of the circle |
| 34A60 | Ordinary differential inclusions |
| 34K45 | Functional-differential equations with impulses |
| 47H04 | Set-valued operators |
| 47H11 | Degree theory for nonlinear operators |
Keywords:
cycle coexistence theorems; admissible circle maps; periodic orbits; irreducible orbits of coincidences; topological degree; impulsive differential inclusions; subharmonic periodic solutionsReferences:
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