A natural constraint approach to normalized solutions of nonlinear Schrodinger equations and systems

The paper deals with the existence of normalized solutions to the system {-Delta u - lambda(1)u = mu(1)u(3) + beta uv(2) in R-3 -Delta nu - lambda(2 nu) = mu(2)nu(3) + beta u(2)nu in R-3 integral(R3) u(2) = a(1)(2) and integral(3)(R) v(2) = a(2)(2) for any mu 1,mu 2,a1 a2 > 0 and beta < 0 prescribed. We present a new approach that is based on the introduction of a natural constraint associated to the problem. We also show that, as beta -> -infinity, phase separation occurs for the solutions that we find. Our method can be adapted to scalar nonlinear Schrodinger equations with normalization constraint, and leads to alternative and simplified proofs to some results already available in the literature. (C) 2017 Elsevier Inc. All rights reserved.