On the existence of ground state solutions to nonlinear Schoedinger equations with multisingular inverse-square anisotropic potentials

TL;DR

This paper investigates conditions under which ground state solutions exist for nonlinear Schrödinger equations with complex anisotropic inverse-square singular potentials, addressing both unbounded and bounded domain cases.

Contribution

It provides new criteria for the existence of ground states considering multiple anisotropic inverse-square singularities in nonlinear Schrödinger equations.

Findings

Conditions on singularity strength, location, and orientation for solution existence.

Existence results in both the entire space and bounded domains.

Analysis of the Rayleigh quotient minimization problem.

Abstract

A class of nonlinear Schroedinger equations with critical power-nonlinearities and potentials exhibiting multiple anisotropic inverse square singularities is investigated. Conditions on strength, location, and orientation of singularities are given for the minimum of the associated Rayleigh quotient to be achieved, both in the whole $\R^N$ and in bounded domains.