Normalized solutions of 𝐿²-supercritical NLS equations on compact metric graphs

Abstract

This paper is devoted to the existence of non-trivial bound states of prescribed mass for the mass-supercritical nonlinear Schrödinger equation on compact metric graphs. The investigation is based upon a min-max principle for some constrained functionals which combines the monotonicity trick and second-order information on the Palais–Smale sequences, and upon the blow-up analysis of bound states with prescribed mass and bounded Morse index.