A sharper energy method for the localization of the support to some stationary Schr{\"o}dinger equations with a singular nonlinearity

TL;DR

This paper introduces an improved energy method to precisely localize the support of solutions to stationary Schr{"o}dinger equations with singular nonlinearities, advancing analytical techniques in quantum mechanics.

Contribution

It develops a sharper energy approach for support localization in Schr{"o}dinger equations with singular nonlinearities, improving upon previous methods.

Findings

Proves the compactness of the solution support.

Introduces a refined energy method for analysis.

Enhances existing techniques for nonlinear Schr{"o}dinger equations.

Abstract

We prove the compactness of the support of the solution of some stationary Schr{\"o}dinger equations with a singular nonlinear order term. We present here a sharper version of some energy methods previously used in the literature and, in particular, by the authors.