Ordinary Differential Equations II

Course content

Nonlinear Periodic Systems: Limit Sets; Poincare-Bendixon Theorem. Linearization Near Periodic Orbits; Method of Small Parameters in Noncritical Case; Orbital stability. Bifurcation: Bifurcation of Fixed Points; The Saddle-Node Bifurcation; The Transcritical Bifurcation; The Pitchfork Bifurcation; Hopf Bifurcation; Branching of Periodic Solutions for Nonautonomous Systems. Boundary Value Problems: Linear Differential Operators; Boundary Conditions; Existence of Solutions of BVPs; Adjoint Problems; Eigenvalues and Eigenfunctions for Linear Differential Operators; Green's Function of a Linear Differential Operator.