@article{Niu2026, 
author = {Huiling Niu and Junshan Liu and Jiayin Liu and Jun Zheng},
title = {Infinitely many small energy solutions for the Schrödinger-Poisson equations with magnetic field},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {12397-12413},
keywords = {Schrödinger-Poisson equation, magnetic field, ground state solution, infinitely many solutions},
url = {https://www.sciopen.com/article/10.3934/math.2026509},
doi = {10.3934/math.2026509},
abstract = {In this paper, we consider the following Schrödinger-Poisson equations with magnetic field     (  −  i  ∇  −  A  (  x  )      )    2    u  +  θ  (      |    x            |              −      1        ∗      |    u            |        2    )  u  =  f  (      |    u            |        2    )  u  ,    u  ∈      H    1    (            R              3        ,      C    )  ,where    i is the imaginary unit and    θ  ≥  0. The function    A  :            R              3        →            R              3       denotes a magnetic potential, and    V  :            R              3        →      R   is a continuous potential. First, we establish the existence of ground state solutions without imposing the strict monotonicity condition and Ambrosetti-Rabinowitz condition. Then using the dual fountain theorem, we obtain the existence of infinitely many small energy solutions. Our results extend some recent work in the literature.}
}