content_image/318206.jpg content_image/318207.jpg content_image/318209.jpg content_image/318208.jpg content_image/318211.jpg content_image/318210.jpg
Finally, we rewrite our inequality with z instead of u . By the relation 

<img src='content_image/318206.jpg'>

we see that there exist positive constants C$_{9}$ = C$_{9}$ ( γ ) and s$_{0}$ > s$_{2}$ ( γ ) such that for all s > s$_{0}$, 

<img src='content_image/318207.jpg'>

We complete the proof of Theorem 1. 

## 4. PROOF OF THEOREM 1 

Since u itself does not satisfy (3.6), in order to apply Proposition 1, we have to introduce a cut-off function. Moreover, we need to introduce several notations. We set 

<img src='content_image/318209.jpg'>

<img src='content_image/318208.jpg'>

By x$_{0}$ / ∈ D , we see that r > 0. We choose ρ > 1 sufficiently large so that 

By (4.3) and the assumption on L, we have 

<img src='content_image/318211.jpg'>

<img src='content_image/318210.jpg'>

