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

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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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