10 citations · 16 across the 4 of their papers we have counts for
7 papers
A minimal mass blow-up solution on a nonlinear quantum star graph
François Genoud, Stefan Le Coz, Julien Royer
We construct a finite-time blow-up solution to the mass-critical focusing nonlinear Schrödinger equation on a metric star graph with an arbitrary number of edges. We show that all…
Extrema of the dynamic pressure in a solitary wave
François Genoud
We study the dynamic pressure in an irrotational solitary wave propagating at the surface of water over a flat bed, under the influence of gravity. We consider the nonlinear regime…
Classification of minimal mass blow-up solutions for an critical inhomogeneous NLS
Vianney Combet, François Genoud
We establish the classification of minimal mass blow-up solutions of the critical inhomogeneous nonlinear Schrödinger equation \[ i\partial_t u + Δu + |x|^{-b}|u|^{\frac{4-2b…
Orbitally stable standing waves for the asymptotically linear one-dimensional NLS
François Genoud
In this article we study the one-dimensional, asymptotically linear, non-linear Schrödinger equation (NLS). We show the existence of a global smooth curve of standing waves for thi…
Landesman-Lazer conditions at half-eigenvalues of the p-Laplacian
François Genoud, Bryan P. Rynne
We study the existence of solutions of the Dirichlet problem {gather} -ϕ_p(u')' -a_+ ϕ_p(u^+) + a_- ϕ_p(u^-) -λϕ_p(u) = f(x,u), \quad x \in (0,1), \label{pb.eq} \tag{1} u(0)=u(1)=0…
Bifurcation along curves for the p-Laplacian with radial symmetry
François Genoud
We study the global structure of the set of radial solutions of a nonlinear Dirichlet problem involving the p-Laplacian with p>2, in the unit ball of , $N \ges 1$. We show tha…
Global bifurcation for asymptotically linear Schrödinger equations
François Genoud
We prove global asymptotic bifurcation for a very general class of asymptotically linear Schrödinger equations \begin{equation}\label{1} \{{array}{lr} \D u + f(x,u)u = \lam u \quad…