Stability of bifurcating periodic solutions of differential inequalities in ℝ3
- Kučera, Milan
2010 Mathematics Subject Classification
- 34A40 58F14 34C25 58F10
- Ordinary differential inequality, bifurcation of periodic solutions, stability, attractivity
A bifurcation problem for the inequality U (t) ∈ K ⋀ (U̇ (t) - AλU(t) - G(λ,U(t)), V - U(t)) ≥ 0 for all V ∈ K, a. a. t ∈[0,T) is considered, where K is a closed convex cone in ℝ3 , Aλ a real 3 x 3 matrix, λ a real parameter, G a small perturbation. We investigate small periodic solutions bifurcating at λ0 from the branch of trivial solutions and corresponding to parameters λ for which the trivial solution is unstable. It is proved that these solutions are stable or they are contained in a certain attracting set Aλ if zero is stable as the solution of our inequality with λ = λ0.