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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 = ρ_n(x)|u|^{p-2}u, \quad n \in \mathbb{N}. \qquad (*…
On the defocusing stationary nonlinear Schrödinger equation on metric graphs
Élio 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 t…
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 a…