Asymptotically autonomous differential equations in the plane. II: Stricter Poincaré/Bendixson type results. (English) Zbl 0811.34037
Summary: [For part I see Rocky Mt. J. Math. 24, No. 1, 351-380 (1994; Zbl 0811.34036, see the preceding review).]
We consider planar asymptotically autonomous ordinary differential equations and their limit equations. We show that the \(\omega\)-limit sets of an asymptotically autonomous equation get very close to having the same properties (of Poincaré/Bendixson type) as the \(\omega\)-limit sets of the corresponding limit equation provided that the non-autonomous perturbation decreases to 0 fast enough as time tends to infinity.
We consider planar asymptotically autonomous ordinary differential equations and their limit equations. We show that the \(\omega\)-limit sets of an asymptotically autonomous equation get very close to having the same properties (of Poincaré/Bendixson type) as the \(\omega\)-limit sets of the corresponding limit equation provided that the non-autonomous perturbation decreases to 0 fast enough as time tends to infinity.
MSC:
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
