In this article, we study the following fractional Schrödinger equation with electromagnetic fields and critical growth
(-△)Asu + V (x)u = |u|2s*-2u + λf(x,|u|2)u, x ∈ RN,
where (-△)As is the fractional magnetic operator with 0 < s < 1, N > 2s, λ > 0, 2s* = 2N/(N-2s), f is a continuous function, V ∈ C(RN, R) and A ∈ C(RN, RN) are the electric and magnetic potentials, respectively. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by Nehari method.
Quanqing LI
,
Wenbo WANG
,
Kaimin TENG
,
Xian WU
. GROUND STATES FOR FRACTIONAL SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND CRITICAL GROWTH[J]. Acta mathematica scientia, Series B, 2020
, 40(1)
: 59
-74
.
DOI: 10.1007/s10473-020-0105-0
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