Lecture 2 (video-conference)

22 Abril 2020, 14:30 • Maria Teresa Faria da Paz Pereira

The classical example x'(t)=-ax(t-r) (r>0,a in R) (continuation): necessary and sufficient condition for oscillation of all solutions. Some references and results for further reading.
Criteria for positivity and comparison of solutions for DDEs with one (or more) discrete delays and for distributed) delays: positivity and Smith's quasimonotone conditions.

This lecture took place on Tuesday, April 28, from 17h to 19h.

Lecture 1 (video-conference)

15 Abril 2020, 14:30 • Maria Teresa Faria da Paz Pereira

Presentation of the course and main references.
Delay differential equations (DDEs): motivation and examples; phase space and notation; similar aspects and main differences between ODEs and DDEs.

The method of steps.

The classical example of de equation x′(t) = −βx(t − r) (r > 0, β ∈ IR): solutions of exponential form and characteristic equation. Real characteristic roots; pure imaginary roots and complex roots with positive real part.

This lecture took place on Tuesday, April 21, from 17h to 19h.

Fractional differential equations. Stability of periodic orbits.

8 Abril 2020, 14:30 • Maria Carlota da Rocha Xavier Rebelo Gonçalves

Fractional differential equations (presentation by Catharine Lo)

Degree theory

1 Abril 2020, 14:30 • Maria Carlota da Rocha Xavier Rebelo Gonçalves

Degree theory (cont) Exposition by Catharine Lo.

Degree theory

25 Março 2020, 14:30 • Maria Carlota da Rocha Xavier Rebelo Gonçalves

Degree theory in finite and infinite dimensions. Applications. Exposition done by Francisco Agostinho. The class took place in the 1st april.