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Research

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2009

Evaluation »

[27 Jul 2009 | No Comment | 618 views]

I was member of the evaluation committee (as supervisor) of the PhD of Manuela Rodrigues with the thesis “Soluções exactas e numéricas para equações de difusão-reacção com termo de convecção“, on 27 July 2009, at the Department of Mathematics of the University of Aveiro.

Seminars and Talks »

[24 Jul 2009 | No Comment | 360 views]

I gave the talk “Four solutions for an elliptic equation with critical exponent and singular term” at Equadiff 12, July 20-24, 2009, Brno, Czech Republic.

Abstract
We show, under some conditions, that the Dirichlet problem

-\Delta u - {\lambda\over {|x|^2}}u = |u|^{2^{\ast}-2}u  + \mu|x|^{\alpha-2}u + f(x) a.e. on \Omega\backslash\{0\} with u\in H_0^1(\Omega),

has four nontrivial solutions where at least one of solutions is sign changing. We assume that 0\in \Omega\subset\mathbb{R}^N (with N\geq 3) is a bounded domain with smoothboundary, 2^{\ast}:=2N/(N-2) is the critical Sobolev exponent, 0\leq \lambda < \Lambda:=((N-2)/2)^2 and f\in L^\infty(\Omega). These results extend some previous works on the literature, as [1-3]. This is a joint work with Jianqing Chen.
Refs
[1] N. Hirano and N. Shioji, A multiplicity result including a sign changing solution for an inhomogeneous Neumann problem with critical exponent, Proc. Roy. Soc. Edinburgh 137A(2007) 333-347.
[2] D. Kang and Y. Deng, Multiple solutions for inhomogeneous elliptic problems involving critical Sobolev-Hardy exponents, J. Math. Anal. Appl. 60(2005) 729-753.
[3] G. Tarantello, Multiplicity results for an inhomogeneous Neumann problem with critical exponent, Manuscripta Math. 81(1993) 51-78.

Evaluation »

[7 May 2009 | No Comment | 305 views]

I was member of the evaluation committee of the MSc of Joao Sintra, 07 March 2009, at the Department of Mathematics of the University of Coimbra.

Other Activities »

[14 Mar 2009 | No Comment | 364 views]

Participation on the meeting TOWARDS A EUROPEAN VIRTUAL LIBRARY IN MATHEMATICS in Santiago de Compostela – Spain, 13-14th March 2009. The motivation for this initiative has emerged after several joint activities between the European countries participating in the WDML digitization project.
This ESF Preparatory Meeting  should serve for exploring the creation of an European infrastructure for Mathematics, focused on digitization, access to research journals, doctoral dissertations and bibliographical databases. It is hoped that with the aid from ESF, a core group of key players representing the European mathematical community will be established. This group will then promote the idea of, and develop the necessary actions for such a future large scale Europe infrastructure for bibliographical support to research. See further details at http://www.usc.es/~esfmaths/

2008

Evaluation »

[30 Dec 2008 | No Comment | 311 views]

In 2008, I reviewed papers for the international journals:

    • Abstract and Applied Mathematics;
    • Applied Mathematical Letters;
    • Applicable Analysis;
    • Mathematical and Computer Modelling;
    • and Mathematics and Computer Science.

Positions »

[12 Dec 2008 | No Comment | 316 views]

ceicSince 2006, I have been a member of the CEIC.PT, a working subcommittee of CNM. On 12th Dec 2008, I have been appointed the Coordinator of CEIC.PT.