In this paper we prove strong unique continuation for
u
u
satisfying an inequality of the form
|
△
m
u
|
≤
f
(
x
,
u
,
D
u
,
⋯
,
D
k
u
)
|\triangle ^m u| \leq f(x,u,Du,\cdots ,D^ku)
, where
k
k
is up to
[
3
m
/
2
]
[3m/2]
. This result gives an improvement of a work by Colombini and Grammatico (1999) in some sense. The proof of the main theorem is based on Carleman estimates with three-parameter weights
|
x
|
2
σ
1
(
log
|
x
|
)
2
σ
2
exp
(
β
2
(
log
|
x
|
)
2
)
|x|^{2\sigma _1}(\log |x|)^{2\sigma _2}\!\exp (\frac {\beta }{2}(\log |x|)^2)
.