Carrying on the discussion initiated in Dovetta and Tentarelli (Ground states of the L^2-critical NLS equation with localized nonlinearity on a tadpole graph, 2018. arXiv:1804.11107 [math.AP]), we investigate the existence of ground states of prescribed mass for the L^2-critical NonLinear Schrödinger Equation on noncompact metric graphs with localized nonlinearity. Precisely, we show that the existence (or nonexistence) of ground states mainly depends on a parameter called reduced critical mass, and then we discuss how the topological and metric features of the graphs affect such a parameter, establishing some relevant differences with respect to the case of the extended nonlinearity studied by Adami et al. (Commun Math Phys 352(1):387–406, 2017). Our results rely on a thorough analysis of the optimal constant of a suitable variant of the L 2 -critical Gagliardo–Nirenberg inequality.

L2 -critical NLS on noncompact metric graphs with localized nonlinearity: topological and metric features / Dovetta, Simone; Tentarelli, Lorenzo. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 58:3(2019). [10.1007/s00526-019-1565-5]

L2 -critical NLS on noncompact metric graphs with localized nonlinearity: topological and metric features

Dovetta Simone;Tentarelli Lorenzo
2019

Abstract

Carrying on the discussion initiated in Dovetta and Tentarelli (Ground states of the L^2-critical NLS equation with localized nonlinearity on a tadpole graph, 2018. arXiv:1804.11107 [math.AP]), we investigate the existence of ground states of prescribed mass for the L^2-critical NonLinear Schrödinger Equation on noncompact metric graphs with localized nonlinearity. Precisely, we show that the existence (or nonexistence) of ground states mainly depends on a parameter called reduced critical mass, and then we discuss how the topological and metric features of the graphs affect such a parameter, establishing some relevant differences with respect to the case of the extended nonlinearity studied by Adami et al. (Commun Math Phys 352(1):387–406, 2017). Our results rely on a thorough analysis of the optimal constant of a suitable variant of the L 2 -critical Gagliardo–Nirenberg inequality.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2771912