Aula 3

19 Novembro 2018, 15:30 • Maria Teresa Faria da Paz Pereira

Statements of the general results about existence and existence and uniqueness of local solutions for an abstract DDE x'(t)=f(t,x_t); proof of the existence and uniqueness theorem only in the case of f(t,\phi) continuous and Lipschitzian relative to \phi in each bounded set of $\R\times C([-r,0],\R^n), by using the contraction principle (rather than Schauder's fixed point theorem).

Consequences: continuous dependence of solutions relative to initial conditions; continuation of solutions (for the future).

Definitions of stabilities (according to Lyapunov); geometrical interpretation.

(Esta aula foi leccionada em português, no dia 23/11/18 e teve a duração de  cerca de 2 horas).