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This is a Quantitative Study study.

October 8, 2025Open Access

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

Key Points

Ground state solutions exist in the (2,q)-Laplacian framework, with distinct behaviors in various regimes.
Key results show the establishment of asymptotic behaviors and distinguish between mass-critical and mass-supercritical cases.
Constrained variational techniques are employed for proofs, ensuring sharp existence results for ground states.
Multiplicity of bound states with prescribed mass reinforces foundational concepts in the study of Schrödinger equations.

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.

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