Lecture 3

20 Novembro 2017, 15:30 • Maria Teresa Faria da Paz Pereira

Criteria for positivity and comparison of solutions for DDEs with (both discrete and distributed) delays: positivity and Smith's quasimonotone conditions. 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).
(This class took place on Wednesday Nov. 15, 2017, from 18h00 to 19h30.)