59 citations · 382 across the 19 of their papers we have counts for
20 papers
The effect of a distribution potential on a quantum mechanical particle in a box
Pedro Martins Girão, João Pedro Nunes
We study the effect of a distribution potential placed at and multiplied by a parameter on a quantum mechanical particle in an infinite square well over the seg…
Regularity of a double null coordinate system for Kerr-Newman-de Sitter spacetimes
Anne T. Franzen, Pedro M. Girão
We construct a double null coordinate system for Kerr-Newman-de Sitter spacetimes and prove that the two-spheres given by the intersection of the hypersurfa…
Solutions of the wave equation bounded at the Big Bang
Pedro M. Girão, José Natário, Jorge Drumond Silva
By solving a singular initial value problem, we prove the existence of solutions of the wave equation which are bounded at the Big Bang in the Friedmann-Lemaitre-Robert…
On the occurrence of mass inflation for the Einstein-Maxwell-scalar field system with a cosmological constant and an exponential Price law
João L. Costa, Pedro M. Girão, José Natário +1
In this paper we study the spherically symmetric characteristic initial data problem for the Einstein-Maxwell-scalar field system with a positive cosmological constant in the inter…
A family of sharp inequalities for Sobolev functions
Pedro M. Girão
Let , be a smooth bounded domain in , , , $S=\inf\left\{\left. \int_{\mathbb{R}^{N}}|\nabla u|^2\,\right|\,u\in L^{2^*}(\mat…
A sharp inequality for Sobolev functions
Pedro M. Girão
Let , , be a smooth bounded domain in , , and . We prove there…
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
David G. Costa, Pedro M. Girão
Let be a smooth bounded domain in , with , , and . We show that the the exponent plays a crit…
Sign changing solutions for elliptic equations with critical growth in cylinder type domains
Pedro M. Girão, Miguel Ramos
We prove the existence of positive and of nodal solutions for , , where and , for a class of open subsets $Ω…
Convergence of a crystalline algorithm for the motion of a simple closed convex curve by weighted curvature
Pedro M. Girão
Motion by weighted mean curvature is a geometric evolution law for surfaces and represents steepest descent with respect to anisotropic surface energy. It has been proposed that th…
Convergence of a crystalline algorithm for the heat equation in one dimension and for the motion of a graph by weighted curvature
Pedro M. Girão, Robert V. Kohn
Motion by (weighted) mean curvature is a geometric evolution law for surfaces, representing steepest descent with respect to (an)isotropic surface energy. It has been proposed that…
Multibump nodal solutions for an indefinite nonhomogeneous elliptic problem
Pedro M. Girão, José Maria Gomes
We construct multibump nodal solutions of the elliptic equation in , when is large, under appropriate assump…
Multibump nodal solutions for an indefinite superlinear elliptic problem
Pedro M. Girão, José Maria Gomes
We define some Nehari-type constraints using an orthogonal decomposition of the Sobolev space and prove the existence of multibump nodal solutions for an indefinite superli…
The shape of extremal functions for Poincaré-Sobolev-type inequalities in a ball
Pedro M. Girão, Tobias Weth
We study extremal functions for a family of Poincaré-Sobolev-type inequalities. These functions minimize, for subcritical or critical , the quotient ${\|\nabla u\|_2}/{\|u…
Positive solutions to logistic type equations with harvesting
Pedro M. Girão, Hossein Tehrani
We use comparison principles, variational arguments and a truncation method to obtain positive solutions to logistic type equations with harvesting both in and in a…
On the Fučik spectrum of the wave operator and an asymptotically linear problem
Pedro M. Girão, Hossein Tehrani
We study generalized solutions of the nonlinear wave equation with periodic conditions in and homogeneous Dirichlet conditions in , und…
Bifurcation curves of a diffusive logistic equation with harvesting orthogonal to the first eigenfunction
Pedro M. Girão, Mayte Pérez-Llanos
We study the global bifurcation curves of a diffusive logistic equation, when harvesting is orthogonal to the first eigenfunction of the Laplacian, for values of the linear growth…
Bifurcation curves of a logistic equation when the linear growth rate crosses a second eigenvalue
Pedro M. Girão
We construct the global bifurcation curves, solutions versus level of harvesting, for the steady states of a diffusive logistic equation on a bounded domain, under Dirichlet bounda…
On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 3: Mass inflation and extendibility of the solutions
João L. Costa, Pedro M. Girão, José Natário +1
This paper is the third part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system w…
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
João L. Costa, Pedro M. Girão, José Natário +1
This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system…
On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 1: Well posedness and breakdown criterion
João L. Costa, Pedro M. Girão, José Natário +1
This paper is the first part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system w…