14 papers
Classification of radial blow-up at the first critical exponent for the Lin-Ni-Takagi problem in the ball
Denis Bonheure, Jean-Baptiste Casteras, Bruno Premoselli
We investigate the behaviour of radial solutions to the Lin-Ni-Takagi problem in the ball for : \begin{equation*} \left \{ \begin{aligned} - \tr…
Hidden dissipation and convexity for Kimura equations
Jean-Baptiste Casteras, Léonard Monsaingeon
In this paper we establish a rigorous gradient flow structure for one-dimensional Kimura equations with respect to some Wasserstein-Shahshahani optimal transport geometry. This is…
Invariant measures and global well-posedness for a fractional Schrödinger equation with Moser-Trudinger type nonlinearity
Jean-Baptiste Casteras, Léonard Monsaingeon
In this paper, we construct invariant measures and global-in-time solutions for a fractional Schr\" odinger equation with a Moser-Trudinger type nonlinearity $$ i\partial_t u= (-Δ)…
Existence of traveling waves for a fourth order Schr\" odinger equation with mixed dispersion in the Helmholtz regime
Jean-Baptiste Casteras, Juraj Foldes
In this paper, we study the existence of traveling waves for a fourth order Schr\" odinger equations with mixed dispersion, that is, solutions to $$Δ^2 u +βΔu +i V \nabla u +αu =|u…
Bifurcation analysis of the Hardy-Sobolev equation
Denis Bonheure, Jean-Baptiste Casteras, Francesca Gladiali
In this paper, we prove existence of multiple non-radial solutions to the Hardy-Sobolev equation $$\begin{cases} -Δu-\displaystyle\frac γ{|x|^2}u=\displaystyle\frac{1}{|x|^s}|u|^{p…
Singular radial solutions for the Lin-Ni-Takagi equation
Juraj Foldes, Jean-Baptiste Casteras
We study singular radially symmetric solution to the Lin-Ni-Takagi equation for a supercritical power non-linearity in dimension . It is shown that for any ball and any $k…