On the notion of ground state for nonlinear Schrödinger equations on metric graphs

Abstract We compare ground states for the nonlinear Schrödinger equation on metric graphs, defined as global minimizers of action functional constrained Nehari manifold, and least solutions, namely among all solutions to equation. In principle, four alternative cases may take place: do exist (thus coinciding with solutions); not while do; both levels two minimizing problems coincide; are different. show that in context graphs alternatives occur. This is accomplished by a careful analysis doubly variational problems. As by-product, we obtain new multiplicity results positive wide class noncompact graphs.