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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…
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 corresponding…
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 establish…
Constant sign and sign changing NLS ground states on noncompact metric graphs
Colette De Coster, Simone Dovetta, Damien Galant +2
We investigate existence and nonexistence of action ground states and nodal action ground states for the nonlinear Schrödinger equation on noncompact metric graphs with rather gene…
On the notion of ground state for nonlinear Schrödinger equations on metric graphs
Colette De Coster, Simone Dovetta, Damien Galant +1
We compare ground states for the nonlinear Schrödinger equation on metric graphs, defined as global minimizers of the action functional constrained on the Nehari manifold, and leas…