New type of solutions for a critical Grushin-type problem with competing potentials

TL;DR

This paper introduces a novel family of solutions for a critical Grushin-type problem with double potentials, using reduction and Pohozaev identities, with solutions concentrated on specific geometric features of a cylinder.

Contribution

The paper develops a new method to construct solutions for a critical Grushin-type problem with double potentials, focusing on geometric concentration points.

Findings

Solutions concentrated on top and bottom circles of a cylinder

Application of reduction argument and Pohozaev identities

New family of solutions for the problem

Abstract

In this paper, we consider a critical Grushin-type problem with double potentials. By applying the reduction argument and local Poho\u{z}aev identities, we construct a new family of solutions to this problem, which are concentrated at points lying on the top and the bottom circles of a cylinder.