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

2008/02/05 by Veronica Felli, Felli, Veronica
Mathematics · #35B33 #35J20 #35J60 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math.AP #msc:35B33 #msc:35J20 #msc:35J60

paper · pdf · doi:10.48550/arxiv.0802.0578

arxiv created 2008/02/05 · openalex publication_date 2008/02/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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