Publications
Book
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 ,
São Paulo J. Math. Sci. (2024). doi.org/10.1007/s40863-024-00421-y .
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.