Normalized solutions of $L^2$-supercritical NLS equations on compact metric graphs
Xiaojun Chang, Louis Jeanjean, Nicola Soave
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.
Topics & Concepts
Morse codeMonotonic functionBounded functionSupercritical fluidMetric (unit)MathematicsNonlinear systemUpper and lower boundsPure mathematicsMathematical analysisApplied mathematicsMathematical physicsPhysicsQuantum mechanicsComputer scienceOperations managementThermodynamicsEconomicsTelecommunicationsAdvanced Mathematical Physics ProblemsNonlinear Photonic SystemsOpinion Dynamics and Social Influence