Existence, non-existence and blow-up behavior of minimizers for the mass-critical fractional nonlinear Schrödinger equations with periodic potentials

Abstract

We consider the minimizing problem for the energy functional with prescribed mass constraint related to the fractional nonlinear Schrödinger equation with periodic potentials. Using the concentration-compactness principle, we show a complete classification for the existence and non-existence of minimizers for the problem. In the mass-critical case, under a suitable assumption of the potential, we give a detailed description of blow-up behavior of minimizers once the mass tends to a critical value.

arXiv comment25 pages, to appear in Proceedings of the Royal Society of Edinburgh, Section A: Mathematics

References in corpus (6)

• Fractional Schrodinger equation
• Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian
• On the Mass Concentration for Bose-Einstein Condensates with Attractive Interactions
• Boson Stars as Solitary Waves
• The Nonexistence of Vortices for Rotating Bose-Einstein Condensates with Attractive Interactions
• Nonlinear fractional Schrödinger equations in one dimension