Luccas Campos

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20182021

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7 papers · 1 filter

math.AP2021

Scattering for the non-radial inhomogenous biharmonic NLS equation

Luccas Campos, Carlos M. Guzmán

We consider the focusing inhomogeneous biharmonic nonlinear Schrödinger equation in $H^{2} (R^{N})$ , \begin{equation} iu_t + Δ^2 u - |x|^{-b}|u|^αu=0 \end{equation} when $b > 0…

math.AP2021

A Virial-Morawetz approach to scattering for the non-radial inhomogeneous NLS

Luccas Campos, Mykael Cardoso

Consider the focusing inhomogeneous nonlinear Schrödinger equation in $H^{1} (R^{N})$ , $i u_{t} + Δ u + ∣ x ∣^{- b} ∣ u ∣^{p - 1} u = 0,$ when $b > 0$ and $N \geq 3$ in the intercritical ca…

math.AP2021

On the inhomogeneous NLS with inverse-square potential

Luccas Campos, Carlos M. Guzmán

We consider the inhomogeneous nonlinear Schrödinger equation with inverse-square potential in $R^{N}$ $$ i u_t + \mathcal{L}_a u+λ|x|^{-b}|u|^αu = 0,\;\;\mathcal{L}_a=Δ-\fra…

math.AP2020

Threshold solutions for the nonlinear Schrödinger equation

Luccas Campos, Luiz Gustavo Farah, Svetlana Roudenko

We study the focusing NLS equation in $R^{N}$ in the mass-supercritical and energy-subcritical (or intercritical) regime, with $H^{1}$ data at the mass-energy threshold $ \mat…

math.AP2020

Blow up and scattering criteria above the threshold for the focusing inhomogeneous nonlinear Schrödinger equation

Luccas Campos, Mykael Cardoso

We consider the inhomogeneous nonlinear Schrödinger equation (INLS) in $R^{N}$ , $N \geq 1$ , $i \partial_{t} u + Δ u + ∣ x ∣^{- b} ∣ u ∣^{p - 1} u = 0,$ with finite-variance initial d…

math.AP2019

Scattering of radial solutions to the Inhomogeneous Nonlinear Schrödinger Equation

Luccas Campos

We prove scattering below the mass-energy threshold for the focusing inhomogeneous nonlinear Schrödinger equation \begin{equation} iu_t + Δu + |x|^{-b}|u|^{p-1}u=0, \end{equation}…