Work

Existence and Blow Up Behavior of Prescribed Mass Solutions on Large Smooth Domains to the Kirchhoff Equation With Combined Nonlinearities

Year: 2026

Type: article

Abstract: ABSTRACT In this paper, we consider the existence, multiplicity, and the asymptotic behavior of solutions with prescribed mass for the following nonlinear Kirchhoff equation with mixed nonlinearities: where is a large bounded smooth star‐shaped domain or the whole space , , and is the potential. The standard approach based on the Pohozaev identity for obtaining normalized solutions becomes inapplicable in this setting due to the presence of the potential . When , we perform a detailed blow‐up analysis to describe the asymptotic behavior of such solutions as . Furthermore, for and , we also prove that is a bifurcation point in the case .

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.71031

Authors: Xiaolu Lin, Zongyan Lv, Yimin Zhang

Institutions: Jianghan University, University of Science and Technology Beijing, Wuhan University of Technology

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Award: G5378544337