Bifurcation of positive periodic solutions of first-order impulsive differential equations

We give a global description of the branches of positive solutions of first-order impulsive boundary value problem: {u'(t) + a(t) u(t) = lambda f (t, u(t)), t is an element of (0, 1), t not equal t(k), k = 1, ... , p, u(t(k)(+)) = u((t-)(k)) + lambda I-k(u(t(k))), k = 1, ... , p, u(0) = u(1), which is not necessarily linearizable. Where lambda > 0 is a parameter, 0 < t(1) < t(2) < ... < t(p) < 1 are given impulsive points. Our approach is based on the Krein-Rutman theorem, topological degree, and global bifurcation techniques.