@article{Yuan2024, 
author = {Ziqing Yuan and Jing Zhao},
title = {Solutions for gauged nonlinear Schrödinger equations on  R2 involving sign-changing potentials},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {8},
pages = {21337-21355},
keywords = {Schrödinger equation, variational method, sign-changing potentival, Morse theory, Chern-Simons gauge term},
url = {https://www.sciopen.com/article/10.3934/math.20241036},
doi = {10.3934/math.20241036},
abstract = {This study focused on establishing the existence and multiplicity of solutions for gauged nonlinear Schrödinger equations set on the plane with sign-changing potentials. Our findings contribute to the extension of recent advancements in this area of research. Initially, we examined scenarios where the potential function  V is lower-bounded and the function space has a compact embedding into Lebesgue spaces. Subsequently, we addressed more complex cases characterized by a sign-changing potential  V and a function space that fails to compactly embed into Lebesgue spaces. The proofs of our results are based on the Trudinger-Moser inequality, the application of variational methods, and the utilization of Morse theory.}
}