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

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9 papers · 1 filter

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…

math.AP2014★ 23 cited

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 $p \geq 2$ , the quotient ${\|\nabla u\|_2}/{\|u…

math.AP2014★ 21 cited

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 $R^{N}$ and in a…