4 citations · 14 across the 14 of their papers we have counts for
15 papers
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…
Large deviation principle for the stationary solutions of stochastic functional differential equations with infinite delay
Yong Liu, Bin Tang
We investigate the large deviation principle (LDP) of the stationary solutions of stochastic functional differential equations (SFDEs) with infinite delay under small random pertur…
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…