QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS

Existence and uniqueness theory for the solution of systems of differential equations:

a) Volterra and Niemitzky operators in the space of continuous functions.

b) Gronwall-Bellman inequalities.

c) Solution of the equation dx \ dt = Ax + h(t,x(t)), Dini-Hukuhara theorem.

Properties of the fundamental matrices. Stability of differential systems. Perturbation of differential systems (invertible transformations). Toda lattice (first integrals, existence and uniqueness of solutions). The inverse problem of the Jacobi matrices and orthogonal polynomials (relation between the Jacobi matrices and the use of orthogonal polynomials).