# ap.analysis of pdes – Mean Value Inequality with Linear Term

I am having trouble proving this modified mean-value inequality.

Suppose that $$Delta u+cuge 0$$ for $$u:mathbb{R}^nto (0,infty).$$

Prove that there exists constants $$r_0,C>0$$ depending only on $$c$$ so that

$$u(0)le frac{C}{r^n}int_{B(r)}u,mathrm{dVol},$$

for all $$rle r_0$$.

This was mentioned in passing in a paper I was reading (without any reference or any indication on how to prove it).

Any help would be much appreciated!