Normalized Solutions of the Gross-Pitaevskii System with Inhomogeneous Interactions

This paper is devoted to the normalized solutions of the two-dimensional Gross-Pitaevskii system with a microwave field and inhomogeneous interactions. By investigating the relevant 2L -critical constrained variational problem, we get the existence and nonexistence of the normalized solutions under suitable assumptions about the interaction potentials.We establish the existence and nonexistence of minimizers of ( ) , e a γ via a threshold * a , where * a is the square of 2 L -norm of the unique positive solution ofWe also analyze the limiting behavior of the constraint minimizers as * 2 a a  through overcoming the challenges associated with the sign-changing property of the logarithmic convolutions and the impact of inhomogeneous interactions.