Advances in Nonlinear Analysis
Walter de Gruyter GmbH
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In this paper, we are concerned with the existence of multi-bump solutions for a class of semiclassical saturable Schrödinger equations with an density function:
We prove that, with the density function being radially symmetric, for given integer k ≥ 2 there exist a family of non-radial, k-bump type normalized solutions (i.e., with the L2 constraint) which concentrate at the global maximum points of density functions when ε → 0+. The proof is based on a variational method in particular on a convexity technique and the concentration-compactness method.
Wang, X. & Wang, Z. (2019). Normalized multi-bump solutions for saturable Schrödinger equations. Advances in Nonlinear Analysis, 9(1), pp. 1259-1277. Retrieved 7 Feb. 2020, from doi:10.1515/anona-2020-0054