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

TL;DR

This paper investigates ground state solutions of (2,q)-Laplacian Schr"odinger equations with inhomogeneous nonlinearity, establishing existence, non-existence, and multiplicity results across different regimes using variational methods.

Contribution

It provides a comprehensive analysis of ground states for these equations, including sharp existence results and multiplicity of bound states, expanding understanding of nonlinear Schr"odinger equations.

Findings

Existence of ground states in various regimes

Non-existence results in certain parameter ranges

Multiplicity of bound states with prescribed mass

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.