Instituto Superior Técnico

output

20022024

f (R)

modified theories of gravity

1k citations

Showing 2014 · math.APShow all

6 papers · 2 filters

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★ 2 cited

Multibump nodal solutions for an indefinite nonhomogeneous elliptic problem

Pedro M. Girão, José Maria Gomes

We construct multibump nodal solutions of the elliptic equation $- Δ u = a^{+} [λ u + f (\cdot, u)] - μ a^{-} g (\cdot, u)$ in $H_{0}^{1} (Ω)$ , when $μ$ is large, under appropriate assump…

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★ 3 cited

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…

math.AP2014★ 3 cited

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…