Asymptotically autonomous differential equations in the plane. II. Stricter Poincaré/Bendixson type results
Horst R. Thieme · Differential and Integral Equations · 1994
We consider planar asymptotically autonomous ordinary differential equations and their limit equations.We show that thew-limit sets of an asymptotically autonomous equation get very close to having the same properties (of Poincare/Bendixson type) as the w-limit sets of the corresponding limit equation provided that the non-autonomous perturbation decreases to 0 fast enough as time tends to infinity.