On the nonlinear Schr\"{o}dinger-Poisson systems with positron-electron interaction
Abstract
We study the Schr\"{o}dinger-Poisson type system: \begin{equation*} \left\{ \begin{array}{ll} -\Delta u+\lambda u+\left( \mu _{11}\phi _{u}-\mu _{12}\phi _{v}\right) u=% \frac{1}{2\pi }\int_{0}^{2\pi }\left\vert u+e^{i\theta }v\right\vert ^{p-1}\left( u+e^{i\theta }v\right) d\theta & \text{ in }\mathbb{R}^{3}, \\ -\Delta v+\lambda v+\left( \mu _{22}\phi _{v}-\mu _{12}\phi _{u}\right) v=% \frac{1}{2\pi }\int_{0}^{2\pi }\left\vert v+e^{i\theta }u\right\vert ^{p-1}\left( v+e^{i\theta }u\right) d\theta & \text{ in }\mathbb{R}^{3},% \end{array}% \right. \end{equation*}% where with parameters . Novel approaches are employed to prove the existence of a positive solution for including, particularly, the finding of a ground state solution for using established linear algebra techniques and demonstrating the existence of two distinct positive solutions for The analysis here, by employing alternative techniques, yields additional and improved results to those obtained in the study of Jin and Seok [Calc. Var. (2023) 62:72].
Cite
@article{arxiv.2306.17343,
title = {On the nonlinear Schr\"{o}dinger-Poisson systems with positron-electron interaction},
author = {Ching-yu Chen and Yueh-cheng Kuo and Tsung-fang Wu},
journal= {arXiv preprint arXiv:2306.17343},
year = {2023}
}