4 citations · 14 across the 14 of their papers we have counts for
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Stable De Giorgi conjecture of the Allen--Cahn equation in
Yong Liu, Tianci Luo, Kelei Wang +3
We prove that every bounded stable entire solution of the Allen--Cahn equation in is one-dimensional. As a consequence, the full De Giorgi conjecture in i…
Free boundary regularity in obstacle problems with a degenerate forcing term
Yong Liu
In this paper, we consider the properties of a special free boundary point in the following obstacle problem: The Laplacian of u equals f(x) multiplied by the characteristic functi…
Stable solutions of Yang-Mills-Higgs model in
Yong Liu, Juncheng Wei, Zikai Ye
We give a positive answer to the conjecture of Liu-Ma-Wei-Wu in \cite{LMWW} that the family of entire solutions to the -Yang-Mills-Higgs equation constructed by the gluing me…
On Dancer's conjecture for stable solutions with sign-changing nonlinearity
Yong Liu, Kelei Wang, Juncheng Wei +1
We establish a Liouville type result for stable solutions for a wide class of second order semilinear elliptic equations in with sign-changing nonlinearity . Un…
Bouncing Jacobi fields and the Allen-Cahn equation on surfaces
Yong Liu, Frank Pacard, Juncheng Wei
The Allen-Cahn functional is a well studied variational problem which appears in the modeling of phase transition phenomenon. This functional depends on a parameter $\varepsilon >0…
From KP-I lump solution to travelling waves of Gross-Pitaevskii equation
Yong Liu, Zhengping Wang, Juncheng Wei +1
Let be an nondegenerate lump solution to KP-I (Kadomtsev-Petviashvili-I) equation $$\partial_x^4q-2\sqrt{2}\partial_x^2q-3\sqrt{2}\partial_x((\partial_xq) ^2)-2\partial_y^…
Entire solutions of the magnetic Ginzburg-Landau equation in
Yong Liu, Xinan Ma, Juncheng Wei +1
We construct entire solutions of the magnetic Ginzburg-Landau equations in dimension 4 using Lyapunov-Schmidt reduction. The zero set of these solutions are close to the minimal su…
Generalized Adler-Moser Polynomials and Multiple vortex rings for the Gross-Pitaevskii equation
Weiwei Ao, Yehui Huang, Yong Liu +1
New finite energy traveling wave solutions with small speed are constructed for the three dimensional Gross-Pitaevskii equation \begin{equation*} iΨ_t= ΔΨ+(1-|Ψ|^2)Ψ, \end{equation…
Stability of the saddle solutions for the Allen-Cahn equation
Yong Liu, Kelei Wang, Juncheng Wei
We are concerned with the saddle solutions of the Allen-Cahn equation constructed by Cabré and Terra \cite{C,C2} in . These so…
Half space theorem for the Allen-Cahn equation and related problems
Francois Hamel, Yong Liu, Pieralberto Sicbaldi +2
In this paper we obtain rigidity results for a bounded non-constant entire solution of the Allen-Cahn equation in , whose level set is contained in a ha…
Nondegeneracy, Morse Index and Orbital Stability of the Lump Solution to the KP-I Equation
Yong Liu, Juncheng Wei
Let be the lump solution of the KP-I equation We show that this solution…
Global minimizers of the Allen-Cahn equation in dimension
Yong Liu, Kelei Wang, Juncheng Wei
We prove the existence of global minimizers of Allen-Cahn equation in dimensions and above. More precisely, given any strictly area-minimizing Lawson's cones, there are global…
On Helmholtz equation and Dancer's type entire solutions for nonlinear elliptic equations
Yong Liu, Juncheng Wei
Starting from a bound state (positive or sign-changing) solution to $$ -Δω_m =|ω_m|^{p-1} ω_m -ω_m \ \ \mbox{in}\ \R^n, \ ω_m \in H^2 (\R^n)$$ and solutions to the Helmholtz equati…
The classification of four end solutions of the Allen-Cahn equation on the plane
Frank Pacard, Michal Kowalczyk, Yong Liu
An entire solution of the Allen-Cahn equation , where has exactly three zeros at and 0, is balanced and odd, e.g. , is called a -ended solut…