Ground state solutions of a class of (2,q)-Laplacian Schr\"odinger equations with inhomogeneous nonlinearity

Abstract

In this paper, we systematically investigate the ground state solutions of a class of (2,q)-Laplacian Schr\"odinger equations with inhomogeneous nonlinearity. By analyzing global and local constrained variational problems, we establish the existence, non-existence, and asymptotic behavior of ground states, addressing the mass-subcritical,mass-critical, and mass-supercritical regimes. As a byproduct, we prove a multiplicity of bound states with prescribed mass. Some of our existence results are sharp. The proofs are based primarily on constrained variational techniques.