Non-existence and behaviour at infinity of solutions of some elliptic equations
Shu-Yu Hsu · Discrete and Continuous Dynamical Systems · 2004
When $\alpha\le 2\beta$, we will prove the non-existence ofsolutions of the equation $\Delta v+\alpha e^v+\beta(x\cdot abla v)e^v=0$ in $R^2$ which satisfy $\gamma=\int_{R^2}e^vdx/(2\pi) 0$. When $\alpha>2\beta$, we will prove thatif $v$ is a solution of the above equation, then there existconstants $02$ and $\gamma<\alpha$.