Limit behavior of attractive Bose-Einstein condensates passing an obstacle

In this paper, we mainly investigate ground states of trapped attractive Bose-Einstein condensates (BEC) passing an obstacle in the plane, which can be described by an L-2-critical constraint minimization problem in an exterior domain Omega = R-2\omega, where the bounded convex domain omega subset of R-2 with smooth boundary denotes the region of the obstacle. It is shown that minimizers (i.e. ground states) exist, if and only if the interaction strength a satisfies a < a* = parallel to Q parallel to(2)(2), where Q > 0 is the unique positive radial solution of Delta u - u + u(3) = 0 in R-2. If the trapping potential V(x) attains its global minima only along the whole boundary partial derivative Omega, the limit behavior of minimizers is analyzed as a NE arrow a* by employing the Pohozaev identity and the delicate energy analysis, where the mass concentration occurs at the flattest critical point of V (x) on a partial derivative Omega. (C) 2020 Published by Elsevier Inc.