On the elliptic equations Δ𝑢=𝐾(𝑥)𝑢^{𝜎} and Δ𝑢=𝐾(𝑥)𝑒^{2𝑢}

Cheng, Kuo-Shung; Lin, Jenn-Tsann

doi:10.1090/S0002-9947-1987-0911088-1

On the elliptic equations $\Delta u=K(x)u^ \sigma$ and $\Delta u=K(x)e^ {2u}$
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Trans. Amer. Math. Soc. 304 (1987), 639-668 Request permission

Abstract:

We give some nonexistence results for the equations $\Delta u = K(x){u^\sigma }$ and $\Delta u = K(x){e^{2u}}$ for $K(x) \geqslant 0$.

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