Publications

Book

• Introdução à Análise Complexa, Séries de Fourier e Equações Diferenciais, IST Press, Julho de 2014.

Papers

• The effect of a delta distribution potential on a quantum mechanical particle in a box, with João Pedro Nunes, submitted.
• Regularity of a double null coordinate system for Kerr-Newman-de Sitter spacetimes, with A.T. Franzen, submitted.
• Higher order linear stability and instability of Reissner-Nordström's Cauchy horizon, with J.L. Costa, Anal. Math. Phys. 10 (2020), 40.
• Solutions of the wave equation bounded at the Big Bang, with J. Natário and J.D. Silva, Class. Quantum Grav. 36 (2019) 075016.
• On the occurrence of mass inflation for the Einstein-Maxwell-scalar field system with a cosmological constant and an exponential Price law, with J.L. Costa, J. Natário and J.D. Silva, Commun. Math. Phys. (2018) 361: 289.
• On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 3: Mass inflation and extendibility of the solutions, with J.L. Costa, J. Natário and J.D. Silva, Ann. PDE (2017) 3: 8. doi:10.1007/s40818-017-0028-6.
• On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 2: Structure of the solutions and stability of the Cauchy horizon, with J.L. Costa, J. Natário and J.D. Silva, Commun. Math. Phys. 339 (2015), 903-947.
• On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 1: Well posedness and breakdown criterion, with J.L. Costa, J. Natário and J.D. Silva, Class. Quantum Grav. 32 (2015), 015017.
• Bifurcation curves of a diffusive logistic equation with harvesting orthogonal to the first eigenfunction, with M. Pérez-Llanos, J. Math. Anal. Appl. 403 (2013), 376-390.
• Bifurcation curves of a logistic equation when the linear growth rate crosses a second eigenvalue, Nonlinear Analysis: Theory, Methods & Applications 74 (2011), 94-113.
  Click here to see an extended version of this paper at the arXiv.
• On the Fucik spectrum of the wave operator and an asymptotically linear problem, with H. Tehrani, J. Math. Anal. Appl. 366 (2010), 55-66.
• Positive solutions to logistic type equations with harvesting, with H. Tehrani, J. Differential Equations 247 (2009), 574-595.
• Multibump nodal solutions for an indefinite nonhomogeneous elliptic problem, with J.M. Gomes, Proceedings of the Royal Society of Edinburgh: Section A Mathematics 139 (2009), 797-817.
• Multibump nodal solutions for an indefinite superlinear elliptic problem, with J.M. Gomes, J. Differential Equations 247 (2009), 1001-1012.
• The shape of extremal functions for Poincaré-Sobolev-type inequalities in a ball, with T. Weth, J. Funct. Anal. 237 (2006), 194-223.
• A family of sharp inequalities for Sobolev functions, Adv. in Differential Equations 8 (2003), 641-671.
• A sharp inequality for Sobolev functions, C. R. Math. Acad. Sci. Paris 334 (2002), 105-108.
• Existence and nonexistence of least energy solutions of the Neumann problem for a semilinear elliptic equation with critical Sobolev exponent and a critical lower-order perturbation, with D.G. Costa, J. Differential Equations 188 (2003), 164-202.
• Sign changing solutions for elliptic equations with critical growth in cylinder type domains, with M. Ramos, ESAIM Control Optim. Calc. Var. 7 (2002), 407-419.
• On the exterior Neumann problem involving the critical Sobolev exponent, with J. Chabrowski, Topol. Methods Nonlinear Anal. 23 (2004), 33-43.
• Symmetric solutions of the Neumann problem involving a critical Sobolev exponent, with J. Chabrowski, Topol. Methods Nonlinear Anal. 19 (2002), 1-27.
• The nonlinear Neumann problem and sharp weighted Sobolev inequalities, with J. Chabrowski, Colloq. Math. 88 (2001), 193-213.
• Convergence of a crystalline algorithm for the motion of a simple closed convex curve by weighted curvature, SIAM J. Numer. Anal. 32 (1995), 886-899.
• Convergence of a crystalline algorithm for the heat equation in one dimension and for the motion of a graph by weighted curvature, with R.V. Kohn, Numer. Math. 67 (1994), 41-70.

Proceedings

• Cauchy horizon stability and mass inflation with a cosmological constant, with J.L. Costa, J. Natário and J.D. Silva, Proceedings of the Spanish Relativity Meeting (ERE 2014): almost 100 years after Einstein's revolution, 1–5 September 2014, Valência, Spain, 2015. Journal of Physics: Conference Series, 600 (2015), 012031.
• The crystalline algorithm for computing motion by curvature, with R.V. Kohn, in Variational methods for discontinuous structures, Proceedings of the International Conference held in Como, September 8-10, 1994, edited by R. Serapioni and F. Tomarelli, 7-18, Progr. Nonlinear Differential Equations Appl., 25, Birkhäuser, 1996.