Front blocking and propagation in cylinders with varying cross section [PDF]
, 2015 In this paper we consider a bistable reaction-diffusion equation in unbounded domains and we investigate the existence of propagation phenomena, possibly partial, in some direction or, on the contrary, of blocking phenomena.
Berestycki, Henri +2 more
core +6 more sources
Plane-like minimizers for a non-local Ginzburg-Landau-type energy in a periodic medium [PDF]
, 2017 We consider a non-local phase transition equation set in a periodic medium and we construct solutions whose interface stays in a slab of prescribed direction and universal width.
Cozzi, Matteo, Valdinoci, Enrico
core +3 more sources
Radial Symmetry of Entire Solutions of a Biharmonic Equation with Supercritical Exponent
Advanced Nonlinear Studies, 2019 Necessary and sufficient conditions for a regular positive entire solution u of a biharmonic ...
Guo Zongming, Wei Long
doaj +1 more source
Existence of stable solutions to $(-\Delta)^m u=e^u$ in $\mathbb{R}^N$ with $m \geq 3$ and $N > 2m$
, 2015 We consider the polyharmonic equation $(-\Delta)^m u=e^u$ in $\mathbb{R}^N$ with $m \geq 3$ and $N > 2m$. We prove the existence of many entire stable solutions.
Huang, Xia, Ye, Dong
core +2 more sources
Classification of global solutions of a free boundary problem in the plane [PDF]
, 2022 We classify nontrivial, nonnegative, positively homogeneous solutions of the equation \begin{equation*} \Delta u=\gamma u^{\gamma-1} \end{equation*} in the plane.
Dipierro, Serena +2 more
core
Remarks on two fourth order elliptic problems in whole space
, 2014 We are interested in entire solutions for the semilinear biharmonic equation $\Delta^{2}u=f(u)$ in $\R^N$, where $f(u)=e^{u}$ or $-u^{-p}\ (p>0)$. For the exponential case, we prove that any classical entire solution verifies $-\Delta u>0$ without any ...
Lai, Baishun, Ye, Dong
core +3 more sources
Properties of entire solutions of some linear PDE's [PDF]
, 2017 In this paper, there are improved sufficient conditions of boundedness of the L-index in a direction for entire solutions of some linear partial differential equations. They are new even for the one-dimensional case and L≡1.
Andriy Bandura +2 more
core +1 more source
Uniqueness and Liouville type results for radial solutions of some classes of k-Hessian equations [PDF]
, 2022 We establish a uniqueness theorem and a Liouville type result for positive radial solutions of some classes of nonlinear autonomous equation with the k-Hessian operator. We also give some interesting qualitative properties of solutions.
Chrouda Mohamed Ben
core
On s-harmonic functions on cones [PDF]
, 2019 We deal with non negative functions which are s-harmonic on a given cone of the n-dimensional Euclidean space with vertex at zero, vanishing on the complementary.
Vita, Stefano
core +2 more sources
Multidimensional entire solutions for an elliptic system modelling phase separation
, 2016 For the system of semilinear elliptic equations \[ \Delta V_i = V_i \sum_{j \neq i} V_j^2, \qquad V_i > 0 \qquad \text{in $\mathbb{R}^N$} \] we devise a new method to construct entire solutions.
Soave, Nicola, Zilio, Alessandro
core +1 more source