MULTIPLICITY AND CONCENTRATION OF SOLUTIONS FOR FRACTIONAL MAGNETIC SCHRÖDINGER-POISSON EQUATION

Houzhi Tang; Jie Shi

doi:10.11948/20250296

2026 Volume 16 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2026 > 16(4): 2190-2217

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Houzhi Tang, Jie Shi. MULTIPLICITY AND CONCENTRATION OF SOLUTIONS FOR FRACTIONAL MAGNETIC SCHRÖDINGER-POISSON EQUATION[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 2190-2217. doi: 10.11948/20250296

Citation:

Houzhi Tang, Jie Shi. MULTIPLICITY AND CONCENTRATION OF SOLUTIONS FOR FRACTIONAL MAGNETIC SCHRÖDINGER-POISSON EQUATION[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 2190-2217. doi: 10.11948/20250296

MULTIPLICITY AND CONCENTRATION OF SOLUTIONS FOR FRACTIONAL MAGNETIC SCHRÖDINGER-POISSON EQUATION

Houzhi Tang^1, ,,
Jie Shi^1,

School of Mathematics and Statistics, Anqing Normal University, Anqing 246133, China

Author Bio: Email: jies2024@163.com(J. Shi)
Corresponding author: Email: houzhitang@163.com(H. Tang)
Fund Project: The authors were supported the Scientific Research Project for the Youth Scholars of Higher Education of Anhui Province (No. 2025AHGXZK40611)

Abstract

Abstract

In this paper, we consider the following fractional Schrödinger-Poisson equation with magnetic fields
$\varepsilon^{2 s}(-\Delta)_{A / \varepsilon}^s u+V(x) u+\varepsilon^{-2}\left(|x|^{-1} *|u|^2\right) u=f\left(|u|^2\right) u \quad \text { in } \mathbb{R}^3,$
where ε > 0 is a small parameter, V(x) : R³ → R and A(x) : R³ → R³ are continuous potentials. Under a local assumption on the potential V, by variational methods, penalization technique and Ljusternik-Schnirelmann theory, we obtain the multiplicity and concentration phenomena of nontrivial solutions of the above problem for ε > 0 small. In this problem, the function f is only continuous, which allow to consider larger classes of nonlinearities in the reaction.
- Schrödinger-Poisson system /
- magnetic field /
- multiple solutions /
- variational methods
MSC: 35B38, 35J20, 35J60

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References

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