Normalized solutions of $L^2$-supercritical NLS equations on compact metric graphs

By Xiaojun Chang, Louis Jeanjean, Nicola Soave. Annales de l'Institut Henri Poincare. Analyse non linéar, 2022

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This paper is devoted to the existence of non-trivial bound states of prescribed mass for the mass-supercritical nonlinear Schr\"odinger equation on compact metric graphs. The investigation is based upon a general variational principle which combines the monotonicity trick and a min-max theorem with second order information, and upon the blow-up analysis of bound states with prescribed mass and bounded Morse index.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8f3f55ad085fb15bfb931add2e1f2794339b7a0b