23 citations · 31 across the 5 of their papers we have counts for
6 papers
Standing wave solutions of a quasilinear Schrödinger equation in the small frequency limit
François Genoud, Simona Rota Nodari
This article is concerned with the quasilinear Schrödinger equation \[ Δu-ωu+|u|^{p-1}u+δΔ(|u|^2)u=0, \] where , and or and . After p…
Stability of Standing Waves for a Nonlinear Klein-Gordon Equation with Delta Potentials
Elek Csobo, François Genoud, Masahito Ohta +1
In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish…
Minimal mass blow-up solutions for the critical NLS with inverse-square potential
Elek Csobo, François Genoud
We study minimal mass blow-up solutions of the focusing critical nonlinear Schrödinger equation with inverse-square potential, \[ i\partial_t u + Δu + \frac{c}{|x|^2}u+|u|^{\…
Instability of an integrable nonlocal NLS
François Genoud
In this note we discuss the global dynamics of an integrable nonlocal NLS on , which has been the object of recent investigation by integrable systems methods. We prove…
Existence of nodal solutions for quasilinear elliptic problems in
Ann Derlet, François Genoud
We prove the existence of one positive, one negative, and one sign-changing solution of a -Laplacian equation on , with a -superlinear subcritical term. Sign-ch…
An inhomogeneous, critical, nonlinear Schrödinger equation
François Genoud
An inhomogeneous nonlinear Schrödinger equation is considered, that is invariant under scaling. The sharp condition for global existence of solutions is established, in…