| back to Research Teams | Differential and Functional Equations Members (Ph. D.) Buescu, Jorge Students Peixe, Telmo Jorge Lucas External Collaborators Keywords Boundary value problems; Delayed population model; Elliptic systems of PDE; Nondeterministic dynamical systems. Objectives 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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