Normalized Solutions for a SchröDinger Equation With Van Der Waals Type Potentials and External Potential: Mass Supercritical

ABSTRACT We study the existence of ground states with prescribed ‐norm for the mass supercritical Schrödinger equation with van der Waals type potentials (that is, two‐body potentials with different width) in the presence of nonsymmetric negative potentials. We prove the existence of normalized ground states at positive energy level under mild assumptions on external potential.