6 papers
The energy of fractional Allen--Cahn layers in dimension one
Alvaro Carballeira, Damien Galant, Javier Gómez-Serrano
We study the energy of the one-dimensional fractional Allen--Cahn layer solution , defined as the unique odd, increasing solution of $(-Δ)^{s} Φ…
Blow-up analysis and a priori bounds for NLS equations on metric graphs
Pablo Carrillo, Colette De Coster, Damien Galant +2
We consider, on a connected metric graph , a family of nonlinear Schrödinger equations $$ -u'' + W_n(x) u + λ_n u = Ï_n(x)|u|^{p-2}u, \quad n \in \mathbb{N}. \qquad…
Normalized solutions of Nehari-Pankov type to mass-supercritical indefinite variational problems
Damien Galant, Tobias Weth
We consider abstract nonlinear equations of the form , where is a self-adjoint operator with compact resolvent on a Hilbert space , is…
On the defocusing stationary nonlinear Schrödinger equation on metric graphs
Ãlio Durand-Simonnet, Damien Galant, Boris Shakarov
We study the defocusing nonlinear Schrödinger equation on noncompact metric graphs under general self-adjoint vertex conditions ensuring the existence of a negative eigenvalue of…
Infinitely many normalized solutions of -supercritical NLS equations on noncompact metric graphs with localized nonlinearities
Pablo Carrillo, Damien Galant, Louis Jeanjean +1
We consider the existence of solutions for nonlinear Schrödinger equations on noncompact metric graphs with localized nonlinearities. In an -supercritical regime, we establis…
An action approach to nodal and least energy normalized solutions for nonlinear Schrödinger equations
Colette De Coster, Simone Dovetta, Damien Galant +1
We develop a new approach to the investigation of normalized solutions for nonlinear Schrödinger equations based on the analysis of the masses of ground states of the correspondin…