ABSTRACT
In this paper, we study the following nonlinear Schrödinger–Newton system
which is a nonlinear system obtained by coupling the linear Schrödinger equation of quantum mechanics with the gravitation law of Newtonian mechanics. Assuming that
is radial and satisfies some algebraic decay at the infinity, we construct infinitely many non-radial positive solutions which have polygonal symmetry with respect to
and
and are even in
for the system above by the Lyapunov-Schmidt reduction method. Moreover, we have overcame some new difficulties caused by the non-local term.
Acknowledgments
The authors would like to thank Chunhua Wang from Central China Normal University for the helpful discussions with her.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Data availability statement
Data sharing is not applicable to this article as no new data were created or analyzed in this study.