Multiple positive solutions for a~Schr\"odinger--Poisson system with critical and supercritical growths
Izvestiya. Mathematics , Tome 87 (2023) no. 1, pp. 29-44
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In this paper, we are concerned with the following Schrödinger–Poisson system
$$
\begin{cases}
-\Delta u+u+\lambda\phi u= Q(x)|u|^{4}u+\mu
\dfrac{|x|^\beta}{1+|x|^\beta}|u|^{q-2}u\text{in }\mathbb{R}^3,
\\
-\Delta \phi=u^{2} \text{in }\mathbb{R}^3,
\end{cases}
$$
where $0 \beta3$, $6$, $Q(x)$ is a positive continuous function
on $\mathbb{R}^3$, $\lambda,\mu>0$ are real parameters. By the variational
method and the Nehari method, we obtain that the system has $k$ positive
solutions.
Keywords:
Schrödinger–Poisson system, critical exponent, supercritical growth.
@article{IM2_2023_87_1_a1,
author = {J. Lei and H. Suo},
title = {Multiple positive solutions for {a~Schr\"odinger--Poisson} system with critical and supercritical growths},
journal = {Izvestiya. Mathematics },
pages = {29--44},
publisher = {mathdoc},
volume = {87},
number = {1},
year = {2023},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2023_87_1_a1/}
}
TY - JOUR AU - J. Lei AU - H. Suo TI - Multiple positive solutions for a~Schr\"odinger--Poisson system with critical and supercritical growths JO - Izvestiya. Mathematics PY - 2023 SP - 29 EP - 44 VL - 87 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IM2_2023_87_1_a1/ LA - en ID - IM2_2023_87_1_a1 ER -
J. Lei; H. Suo. Multiple positive solutions for a~Schr\"odinger--Poisson system with critical and supercritical growths. Izvestiya. Mathematics , Tome 87 (2023) no. 1, pp. 29-44. http://geodesic.mathdoc.fr/item/IM2_2023_87_1_a1/