# A conformal Yamabe problem with potential on the euclidean space

## TL;DR

This paper investigates a Yamabe-type equation with a potential in Euclidean space, establishing conditions for existence and nonexistence of solutions, especially in the radial case, relevant to Ricci solitons.

## Contribution

It introduces a generalized Yamabe problem with potential in Euclidean space and provides new existence and nonexistence results under broad hypotheses.

## Key findings

- Existence of solutions under certain potential conditions
- Nonexistence results for specific potential configurations
- Focus on radial solutions in Euclidean space

## Abstract

We consider, in the Euclidean setting, a conformal Yamabe-type equation related to a potential generalization of the classical constant scalar curvature problem and which naturally arises in the study of Ricci solitons structures. We prove existence and nonexistence results, focusing on the radial case, under some general hypothesis on the potential.