Infinitely many normalized solutions of L²-supercritical NLS equations on noncompact metric graphs with localized nonlinearities

2024/03/16 by Carrillo, Pablo, Galant, Damien, Jeanjean, Louis +1 · 4 citations
#35J60 #47J30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.10959

Abstract

We consider the existence of solutions for nonlinear Schrödinger equations on noncompact metric graphs with localized nonlinearities. In an L²-supercritical regime, we establish the existence of infinitely many solutions for any prescribed mass.

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• Existence and multiplicity of normalized solutions for L²-supercritical Schrödinger equations on noncompact metric graphs with nonlinear point defects
• Nonrelativistic limit of normalized solutions of nonlinear Dirac equations on noncompact metric graphs with localized nonlinearities
• Normalized solutions of L²-supercritical NLS equations on noncompact metric graph with vanishing potential and localized nonlinearities
• Normalized solutions of nonlinear Dirac equations on noncompact metric graphs with localized nonlinearities

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