Asymptotic behavior of solutions to Δ𝑢+𝐾𝑢^{𝜎}=0 on 𝑅ⁿ for 𝑛≥3

Trubek, Jeanne

doi:10.1090/S0002-9939-1989-0987615-2

Asymptotic behavior of solutions to $\Delta u+Ku^ \sigma =0$ on $\textbf {R}^ n$ for $n\geq 3$
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Proc. Amer. Math. Soc. 106 (1989), 953-959 Request permission

Abstract:

The equation $\Delta u + K{u^\sigma } = 0$ is considered in ${R^n}$ for $n \geq 3,K$ a Hölder continuous function and $\sigma$ a positive constant. If $K = O({\left | x \right |^{ - l}})$ for $l > 2$, we determine the asymptotic behavior of bounded solutions. In the case $K$ is nonpositive and $\sigma$ is greater than one, we show that the first term in the asymptotic description may be chosen arbitrarily.

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