128 citations · 524 across the 29 of their papers we have counts for
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Qualitative properties of solutions to mixed-diffusion bistable equations
Denis Bonheure, Földes Juraj, Saldaña Alberto
We consider a fourth-order extension of the Allen-Cahn model with mixed-diffusion and Navier boundary conditions. Using variational and bifurcation methods, we prove results on exi…
Multi-layer radial solutions for a supercritical neumann problem
Denis Bonheure, Massimo Grossi, Benedetta Noris +1
In this paper we study the Neumann problem\begin{equation*}\begin{cases}-Δu+u=u^p \& \text{ in }B\_1 \\u \textgreater{} 0, \& \text{ in }B\_1 \\\partial\_νu=0 \& \text{ on } \parti…
One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in R
Denis Bonheure, François Hamel
In this paper, we prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R N , as well as Liouville type results for some solutions convergin…
On the electrostatic Born-Infeld equation with extended charges
Denis Bonheure, Pietro d'Avenia, Alessio Pomponio
In this paper, we deal with the electrostatic Born-Infeld equation \begin{equation}\label{eq:BI-abs} \tag{} \left\{ \begin{array}{ll} -\operatorname{div}\left(\displa…