Abstract
This paper is concerned with the fractional coupled Schrödinger system. By using the Nehari manifold and fibering map, we obtain the multiplicity and concentration of solutions for the given problem with steep potential wells, where some new estimates will be established. In particular, although there exist concave-convex nonlinearities in the coupled system, it is not necessary to assume that the corresponding Lebesgue norms of the weight functions of the convex terms need to be small enough.
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