## 505 Citations

p-th Kazdan-Warner equation on graph

- Mathematics
- 2016

Let $G=(V,E)$ be a connected finite graph and $C(V)$ be the set of functions defined on $V$. Let $\Delta_p$ be the discrete $p$-Laplacian on $G$ with $p>1$ and $L=\Delta_p-k$, where $k\in C(V)$ is…

Symplectic vortex equations for Kahler cones over Sasakian manifolds

- Mathematics
- 2018

We obtain a Hitchin-Kobayashi-type correspondence for symplectic vortex equations, with the target a Kahler cone over a compact Sasakian manifold. We show that the correspondence reduces to studying…

The Nirenberg problem of prescribed Gauss curvature on $S^2$

- Mathematics
- 2017

We introduce a new perspective on the classical Nirenberg problem of understanding the possible Gauss curvatures of metrics on $S^{2}$ conformal to the round metric. A key tool is to employ the…

Integrable vortex-type equations on the two-sphere

- Mathematics
- 2012

We consider the Yang-Mills instanton equations on the four-dimensional manifold ${S}^{2}\ifmmode\times\else\texttimes\fi{}\ensuremath{\Sigma}$, where $\ensuremath{\Sigma}$ is a compact Riemann…

Geophysics and Stuart vortices on a sphere meet differential geometry

- Computer ScienceCommunications on Pure and Applied Analysis
- 2022

It is proved new existence criteria relevant for the non-linear elliptic PDE of the form M1 valid when ocean surface currents are modeled, as well as several previously known results valid when the parameter regime is changed.

Brouwer degree for Kazdan-Warner equations on a connected finite graph

- MathematicsAdvances in Mathematics
- 2022

Two solutions to Kazdan-Warner’s problem on surfaces

- MathematicsProceedings of the American Mathematical Society
- 2021

In this paper, we study the sign-changing Kazdan-Warner's problem on two dimensional closed Riemannian manifold with negative Euler number $\chi(M)<0$. We show that once, the direct method on convex…

Existence of Kazdan-Warner equation with sign-changing prescribed function

- Mathematics
- 2020

In this paper, we study the following Kazdan-Warner equation with sign-changing prescribed function h −∆u = 8π

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Partial differential equations

- Mathematics
- 1953

Many physical problems involve quantities that depend on more than one variable. The temperature within a “large”1 solid body of conducting material varies with both time and location within the…