Normalized solutions for Schrdinger equations with critical Sobolev exponent and mixed nonlinearities

摘要

In this paper, we consider the following nonlinear Schrodinger equations with mixed nonlinearities: {-Delta u = lambda u + mu vertical bar u vertical bar(q-2) u + vertical bar u(2*-2) u in R-N, u is an element of H-1(R-N), integral(RN) u(2) = a(2), where N >= 3, mu > 0, lambda is an element of R and 2 = 3 and 2 0 large; (3) Precisely asymptotic behaviors of ground states and mountain-pass solutions as mu -> 0 and mu goes to its upper bound. Our studies answer some open questions proposed by Soave in [48]. (C) 2022 Elsevier Inc. All rights reserved.