Normalized ground states of the nonlinear Schrodinger equation with at least mass critical growth

摘要

We propose a simple minimization method to show the existence of least energy solutions to the normalized problem {-Delta u + lambda u = g(u) in R-N, N >= 3, u is an element of H-1 (R-N), integral RN vertical bar u vertical bar(2) dx - rho > 0, where rho is prescribed and (lambda, u) is an element of R xH(1)(R-N) is to be determined. The new approach based on the direct minimization of the energy functional on the linear combination of Nehari and Pohozaev constraints intersected with the closed ball in L-2(R-N) of radius rho is demonstrated, which allows to provide general growth assumptions imposed on g. We cover the most known physical examples and nonlinearities with growth considered in the literature so far as well as we admit the mass critical growth at 0. (C) 2021 Elsevier Inc. All rights reserved.