81 citations · 160 across the 37 of their papers we have counts for
4 papers · 1 filter
Orbitally stable standing waves of a mixed dispersion nonlinear Schrödinger equation
Denis Bonheure, Jean-Baptiste Castéras, Ederson Moreira dos Santos +1
We study the mixed dispersion fourth order nonlinear Schrödinger equation \begin{equation*} %\tag{\protect{4NLS}}\label{4nls} i \partial_t ψ-γΔ^2 ψ+βΔψ+|ψ|^{2σ} ψ=0\ \text{in}\ \R…
Unbounded mass radial solutions for the Keller-Segel equation in the disk
Denis Bonheure, Jean-Baptiste Casteras, Carlos Román
We consider the boundary value problem $$ \left\{ \begin{array}{rcll} -Δu+ u -λe^u&=&0,\ u>0 & \mathrm{in}\ B_1(0)\\ \partial_νu&=&0&\mathrm{on}\ \partial B_1(0), \end{array}\right…
Strong instability of ground states to a fourth order Schrödinger equation
Denis Bonheure, Jean-Baptiste Casteras, Tianxiang Gou +1
In this note we prove the instability by blow-up of the ground state solutions for a class of fourth order Schr\" odinger equations. This extends the first rigorous results on blow…
Existence and non-existence of minimal graphic and -harmonic functions
Jean-Baptiste Casteras, Esko Heinonen, Ilkka Holopainen
We prove that every entire solution of the minimal graph equation that is bounded from below and has at most linear growth must be constant on a complete Riemannian manifold wi…