MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS QUASILINEAR SCHRÖDINGER–POISSON SYSTEM

Lanxin Huang; Jiabao Su

doi:10.11948/20220404

2023 Volume 13 Issue 3

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Lanxin Huang, Jiabao Su. MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS QUASILINEAR SCHRÖDINGER–POISSON SYSTEM[J]. Journal of Applied Analysis & Computation, 2023, 13(3): 1597-1612. doi: 10.11948/20220404

Citation:

Lanxin Huang, Jiabao Su. MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS QUASILINEAR SCHRÖDINGER–POISSON SYSTEM[J]. Journal of Applied Analysis & Computation, 2023, 13(3): 1597-1612. doi: 10.11948/20220404

MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS QUASILINEAR SCHRÖDINGER–POISSON SYSTEM

Lanxin Huang^1,,
Jiabao Su^1, ,

1.
School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

Author Bio: Email: 812419761@qq.com(L. Huang)
Corresponding author: Email: sujb@cnu.edu.cn.(J. Su)
Fund Project: The authors were supported by National Natural Science Foundation of China (12271373, 12171326) and KZ202010028048

Abstract

Abstract

We consider the nonhomogeneous quasilinear Schrödinger–Poisson system
$ \begin{align*} \begin{cases} -\Delta_{p} u+|u|^{p-2}u+\lambda\phi |u|^{p-2}u = |u|^{q-2}u+h(x) & \ \ \ \mathrm{in}\ \mathbb{R}^{3}, \\ -\Delta \phi = |u|^{p} &\ \ \ \mathrm{in}\ \mathbb{R}^{3}, \end{cases} \end{align*} $
where $ 1<p<3 $, $ p<q<p^{*} = \frac{3p}{3-p} $, $ \Delta_{p} u = \hbox{div}(|\nabla u|^{p-2}\nabla u) $, $ \lambda >0 $ and $ h \not = 0 $. Under suitable assumptions on $ h $, the Ekeland's variational principle and the mountain pass theorem are applied to establish the existence of multiple solutions for this system. To the best of our knowledge, this paper is one of the first contributions to the study of the nonhomogeneous quasilinear Schrödinger–Poisson system.
- Nonhomogeneous quasilinear Schrödinger–Poisson system /
- variational methods /
- multiple solutions
MSC: 35J10, 35J50, 35J60, 35J92

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References

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