Action versus energy ground states in nonlinear Schrödinger equations

Abstract We investigate the relations between normalized critical points of nonlinear Schrödinger energy functional and corresponding action on associated Nehari manifold. Our first general result is that ground state levels are strongly related by following duality result: (negative) level Legendre–Fenchel transform level. Furthermore, whenever an exists at a certain frequency, then all states with frequency have same mass too. prove converse in false may fail to be convex. Next we analyze differentiability provide explicit expression involving states. Finally show similar results hold also for local minimizers.