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| Differential and Functional Equations

Members (Ph. D.)

Buescu, Jorge
Domingos, Ana Rute
Duarte, Pedro
EnguiƧa, Ricardo
Faria, Teresa
Margheri, Alessandro
Rebelo, Carlota
Sanchez, Luis


Peixe, Telmo Jorge Lucas
Serpa, Maria Cristina G. Silveira de

External Collaborators

Dalbono, Francesca


Boundary value problems; Delayed population model; Elliptic systems of PDE; Nondeterministic dynamical systems.


The group has consistently been working in ordinary, partial and functional differential equations and dynamical systems. The main topics of our current research are:

- Elliptic equations and systems: qualitative properties and multiplicity of solutions.

- Global stability for n-dimensional functional differential equations;  travelling waves for reaction-diffusion equations with delays; applications to delayed population dynamics models.

- 2nd order non-autonomous scalar differential equations: existence of heteroclinics between two equilibria. One-dimensional versions of field equations. Fourth order boundary value problems: positivity and upper and lower solutions.

- Dynamical systems: spectral stability of Markov Systems, the limit dynamics along the edges of flows in polyhedra, a geometric approach to accessibility, and the relation between fixed points and Lyapounov functions for smooth endomorphisms of the euclidean space. ) Relationship between ODEs and computability. Algebraic aspects of discrete dynamical systems.

- Connected branches of initial points for asymptotic BVPs with applications to heteroclinic and homoclinic solutions.

- Asymptotically linear second order systems.

- ODE models in epidemiology.

- To develop consistently a theory of differential equations and dynamical systems parallel to the classical one taking into account modern computability and complexity.


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