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## ap.evaluation of pdes – Find strictly subharmonic duty that vanishes at infinity

I’m not positive concerning the time period “strictly” subharmonic.

What I need is a duty $psiin C^{infty}(mathbb{R}^3)$ with $Deltapsi>0$ and $limlimits_rightarrowinftypsi(x)=0$.

I attempted a number of instances however quiet failed on the inception. I took $psi=exp(-frac{1}x)-1$ with

$$Deltapsi=frac{1}xexp(-frac{1}x)>0$$

at each level $xnot=0$, and the border worth does vanish, however $Deltapsi(0)=0$.

Also, is that this workable in $mathbb{R}^2$? I need to employ the comparability precept for the elliptic operator Laplacian $Delta$ to disprove it, however that may solely inform me $psi<0$. How can I make employ of the dimension? Or is that this too workable?

Any ameliorate is desired.

The query is too posted on MSE

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