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RESEARCH

Research interests:

Partially supported by the Research Unity Mathematics and Applications of the University of Aveiro (the Functional Analysis and Applications research group) and by the FCT- Foundation for Science and Technology of Portugal by the research project POCI/MAT/55524/2004, the research activity is concerning with the following main topics:

· Existence theory amd qualitative theory to differential inclusions;

· Probabilistic methods applied to the study of differential inclusions;

· Variational and Degree theoretic methods to Nonlinear analysis;

· Existence and multiplicity of solutions to second order boundary value problems with multivalued terms.Existence theory to calculus of variations problems and to minimization of functionals constrained by nonconvex differential inclusions;Non-smooth Analysis and applications to Optimal control and Hamilton - Jacobi Equations.

· Existence and properties of solutions to quasilinear elliptic systems in divergence form.

· Optimal harvesting problems: necessary conditions satisfied by an optimal solution to the harvesting problem and to deal with a competitive scenario, where a large number of small fishing companies harvest the same marine resource.

· Necessary and sufficient condition for the existence of minima for integral functional depending on the gradient with a lagrangean having slow growth and study of the regularity of solutions to minimum problems for integral functional depending on the gradient with Lagrangean having fast growth.

· Controlled Set Motion in a Bounded Domain: eradication and minimum time problems.

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