6 papers · 1 filter
Rigidity of a -curvature-type problem on in every dimension
Changfeng Gui, Yeyao Hu, Tuoxin Li +3
We prove that for every , every solution to the -curvature-type problem $$ αP_N u + (N-1)!\left(1-\frac{e^{Nu}}{\int_{\mathbb{S}^N} e^{Nu}dw}\right)=0 \ \ \ \ \ \mbox{o…
Planar Gross--Pitaevskii traveling waves at every subsonic speed
Changfeng Gui, Shanfa Lai, Guolin Qin +1
For every subsonic speed , we prove the existence of a finite-energy traveling wave for the planar Gross--Pitaevskii equation. This resolves the longstanding proble…
A positive answer to the generalized Chang-Yang conjecture on
Changfeng Gui, Tuoxin Li, Juncheng Wei +1
We prove that for every integer and , Beckner's inequality \[ \fracα{2}\int_{\mathbb{S}^N}u(P_{N}u) dw+(N-1)!\int_{\mathbb{S}^N}u dw-\frac{(N-1)!}{N}\l…
Axially Symmetric Rigidity for a -Curvature-Type Equation on
Changfeng Gui, Tuoxin Li, Juncheng Wei +1
We prove that for every even integer or , every axially symmetric solution to the -curvature-type problem $$ αP_N u + (N-1)!(1-\frac{e^{Nu}}{\int_{\math…
Symmetry breaking for the complex sine-Gordon equation
Shibing Chen, Changfeng Gui, Yong Liu +2
We consider the existence of vortex solutions to the complex sine-Gordon II (CSG2) equation, which can be viewed as an analogy of the Ginzburg-Landau (GL) equation. Using the nontr…
On two-dimensional steady compactly supported Euler flows with constant vorticity
Changfeng Gui, Jun Wang, Wen Yang +1
In this paper, we study the two-dimensional steady compactly supported incompressible Euler equations with free boundaries. We consider flows with constant vorticity that are pertu…