On the stability of periodic solutions for differential equations with a Fredholm operator at the highest derivative

On the basis of a classic Floquet theory variant, the stability of periodic solutions at Andronov-Hopf bifurcation for autonomous nonlinear differential equations of sth order (s≥1) with a degenerate Fredholm operator at the highest derivative in Banach spaces is investigated. Stability criteria based on the perturbation theory and Newton diagram method are suggested.