Pedro M. Girão

activity

20142023

most citedMultibump nodal solutions for an indefinite superlinear elliptic problem

24 citations · 88 across the 11 of their papers we have counts for

collaborators

11 papers

quant-ph2023

The effect of a $δ$ distribution potential on a quantum mechanical particle in a box

Pedro Martins Girão, João Pedro Nunes

We study the effect of a $δ$ distribution potential placed at $x_{0} \geq 0$ and multiplied by a parameter $α$ on a quantum mechanical particle in an infinite square well over the seg…

gr-qc2019

Higher Order Linear Stability and Instability of Reissner-Nordström's Cauchy Horizon

João L. Costa, Pedro M. Girão

We consider smooth solutions of the wave equation, on a fixed black hole region of a subextremal Reissner-Nordström (asymptotically flat, de Sitter or anti-de Sitter) spacetime, wh…

math.AP2014★ 5 cited

A sharp inequality for Sobolev functions

Pedro M. Girão

Let $N \geq 5$ , $a > 0$ , $Ω$ be a smooth bounded domain in $R^{N}$ , $2^{*} = \frac{2 N}{N - 2}$ , $2^{#} = \frac{2 ( N - 1 )}{N - 2}$ and $∣∣ u ∣ ∣^{2} = ∣\nabla u ∣_{2}^{2} + a ∣ u ∣_{2}^{2}$ . We prove there…

math.AP2014★ 9 cited

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 $Ω$ be a smooth bounded domain in $R^{N}$ , with $N \geq 5$ , $a > 0$ , $α \geq 0$ and $2^{*} = \frac{2 N}{N - 2}$ . We show that the the exponent $q = \frac{2 ( N - 1 )}{N - 2}$ plays a crit…

math.AP2014

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 $- Δ u = ∣ u ∣^{p - 2} u + μ ∣ u ∣^{q - 2} u$ , $u \in H_{0}^{1} (Ω)$ , where $μ > 0$ and $2 < q < p = 2 N (N - 2)$ , for a class of open subsets $Ω…

math.AP2014★ 24 cited

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 $H_{0}^{1}$ and prove the existence of multibump nodal solutions for an indefinite superli…