تقرير
Normalized solutions for a fractional Schr\'{o}dinger-Poisson system with critical growth
| العنوان: | Normalized solutions for a fractional Schr\'{o}dinger-Poisson system with critical growth |
|---|---|
| المؤلفون: | He, Xiaoming, Meng, Yuxi, Squassina, Marco |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 35J62, 35J50, 35B65 |
| الوصف: | In this paper, we study the fractional critical Schr\"{o}dinger-Poisson system \[\begin{cases} (-\Delta)^su +\lambda\phi u= \alpha u+\mu|u|^{q-2}u+|u|^{2^*_s-2}u,&~~ \mbox{in}~{\mathbb R}^3,\\ (-\Delta)^t\phi=u^2,&~~ \mbox{in}~{\mathbb R}^3,\end{cases} \] having prescribed mass \[\int_{\mathbb R^3} |u|^2dx=a^2,\] where $ s, t \in (0, 1)$ satisfies $2s+2t > 3, q\in(2,2^*_s), a>0$ and $\lambda,\mu>0$ parameters and $\alpha\in{\mathbb R}$ is an undetermined parameter. Under the $L^2$-subcritical perturbation $q\in (2, 2+\frac{4s}{3})$, we derive the existence of multiple normalized solutions by means of the truncation technique, concentration-compactness principle and the genus theory. For the $L^2$-supercritical perturbation $q\in (2+\frac{4s}{3}, 2^*_s)$, by applying the constrain variational methods and the mountain pass theorem, we show the existence of positive normalized ground state solutions. Comment: 43 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.00464 |
| رقم الأكسشن: | edsarx.2402.00464 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |