Electron. J. Differential Equations, Vol. 2025 (2025), No. 59, pp. 1-20

Minimizers for fractional Schrodinger equations with inhomogeneous perturbation

Lei Zhang, Lintao Liu, Haibo Chen

Abstract:
In this article, we study a constrained minimization problem arising in fractional Schrodinger equations with inhomogeneous term \(m(x)\not\equiv 1\). We obtain the existence and limit behavior of constraint minimizers. The argument relies on energy estimates, blow-up analysis, comparison principle and iteration methods.

Submitted March 28, 2025. Published June 6, 2025.
Math Subject Classifications: 35B44, 35J20, 35J60.
Key Words: Inhomogeneous fractional equation; energy estimate; blow-up analysis; mass concentration.
DOI: 10.58997/ejde.2025.59

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Lei Zhang
School of Mathematics and Statistics
HNP-LAMA, Central South University
Changsha 410083, China
email: math_zl317@163.com
Lintao Liu
Department of Mathematics
North University of China
Taiyuan 030051, China
email: liulintao_math@nuc.edu.cn
Haibo Chen
School of Mathematics and Statistics
HNP-LAMA, Central South University
Changsha 410083, China
email: math_chb@csu.edu.cn

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