Abstract
AbstractWe compare ground states for the nonlinear Schrödinger equation on metric graphs, defined as global minimizers of the action functional constrained on the Nehari manifold, and least action solutions, namely minimizers of the action among all solutions to the equation. In principle, four alternative cases may take place: ground states do exist (thus coinciding with least action solutions); ground states do not exist while least action solutions do; both ground states and least action solutions do not exist and the levels of the two minimizing problems coincide; both ground states and least action solutions do not exist and the levels of the two minimizing problems are different. We show that in the context of metric graphs all four alternatives do occur. This is accomplished by a careful analysis of doubly constrained variational problems. As a by-product, we obtain new multiplicity results for positive solutions on a wide class of noncompact metric graphs.
Funder
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference42 articles.
1. Adami, R., Boni, F., Dovetta, S.: Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs. J. Funct. Anal. 283(1), 109483 (2022)
2. Adami, R., Boni, F., Ruighi, A.: Non-Kirchhoff vertices and nonlinear Schrödinger ground states on graphs. Mathematics 8(4), 617 (2020)
3. Adami, R., Cacciapuoti, C., Finco, D., Noja, D.: Stable standing waves for a NLS on star graphs as local minimizers of the constrained energy. J. Differ. Equ. 260, 7397–7415 (2016)
4. Adami, R., Cacciapuoti, C., Finco, D., Noja, D.: Stationary states of NLS on star graphs. Europhys. Lett. 100(1), 10003 (2012)
5. Adami, R., Serra, E., Tilli, P.: Multiple positive bound states for the subcritical NLS equation on metric graphs. Calc. Var. PDE 58(5), 16 (2019)
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