Work

Normalized Ground State Solutions to HLS Upper Critical Choquard Equation With Mass Critical or Supercritical and Sobolev Critical Growth

Year: 2025

Type: article

Abstract: ABSTRACT This paper is concerned with the following HLS upper critical Choquard equation with mass critical or supercritical and Sobolev critical growth where is a Lagrange multiplier and is the Riesz potential. The novelty of this paper is that, utilizing the classical strategy due to Jeanjean (Nonlinear Analysis: Theory, Methods & Applications, 28(1997), 1633‐1659) and after some subtle energy estimate, we show the existence of mountain pass type normalized ground state solutions for any . In this sense, the novelty of this paper includes three aspects: when , we do not need to add any constraints to the parameter ; meanwhile, the mountain pass type solution happens to be one ground states; in addition, the ‐critical perturbation, that is, is considered, which generalize and improve the recent results.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.11177

Authors: Jianlun Liu, Ziheng Zhang, Hong‐Rui Sun

Institutions: Tiangong University, Lanzhou University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, National Natural Science Foundation of China

Awards: G5601576990, G658636233, G8471141423