In the present paper, we consider the nonlocal Kirchhoff problem
- (ε2a + εb∫R3 |▽u|2)△u + u = Q(x)up, u > 0 in R3,
where a, b > 0, 1 < p < 5 and ε > 0 is a parameter. Under some assumptions on Q(x), we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method, respectly.
Gongbao LI
,
Yahui NIU
. THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK POSITIVE SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATION[J]. Acta mathematica scientia, Series B, 2020
, 40(1)
: 90
-112
.
DOI: 10.1007/s10473-020-0107-y
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