@article{Dong2024, 
author = {Fangyuan Dong},
title = {Multiple positive solutions for the logarithmic Schrödinger equation with a Coulomb potential},
year = {2024},
journal = {Communications in Analysis and Mechanics},
volume = {16},
number = {3},
pages = {487-508},
keywords = {variational method, logarithmic Schrödinger equation, multiple solutions, Coulomb potential},
url = {https://www.sciopen.com/article/10.3934/cam.2024023},
doi = {10.3934/cam.2024023},
abstract = {In this article, we mainly study the global existence of multiple positive solutions for the logarithmic Schrödinger equation with a Coulomb type potential   −Δu+V(ϵx)u=λ(Iα∗|u|p)|u|p−1+ulog⁡u2inR3,where  u∈H1(R3),  ϵ>0,  V is a continuous function with a global minimum, and Coulomb type energies with  0<α<3 and  p≥1. We explore the existence of local positive solutions without the functional having to be a combination of a  C1 functional and a convex semicontinuous functional, as is required in the global case.}
}