Work

Normalized Solutions for a Class of the Nonlinear Elliptic Systems with Mixed-Power Nonlinearities on Bounded Domains

Year: 2026

Type: article

Abstract: In this paper, we discuss the existence of normalized solutions for a class of the nonlinear elliptic systems with mixed-power nonlinearities on bounded domains. When the lower-order nonlinearity is L2-subcritical and the leading term is L2-critical, the global solutions can be found by minimum principle. If the lower-order nonlinearity is L2-subcritical or L2-critical and the leading term is L2-supercritical and Sobolev-subcritical, we can find the local minimum solutions by providing some proper conditions about the parameters. Furthermore, if the lower-order nonlinearity is L2-critical and the leading term is Sobolev-critical, we restore the compactness of a minimizing sequence so that the local solution can be achieved.

Source: Mathematics

DOI: 10.3390/math14213905

Authors: Liang Zhang, Juan Liu, Jing Shao, Qingzhe Wu

Institution: Shenyang University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: National Natural Science Foundation of China, Shenyang Science and Technology Bureau, Department of Science and Technology of Liaoning Province