Mathematical Theory and Applications ›› 2024, Vol. 44 ›› Issue (2): 20-35.doi: 10.3969/j.issn.1006-8074.2024.02.002
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Wang Mei, Suo Hongmin*, Zhang Xuemei, Wang Chenxi
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Abstract:
In this paper we consider the existence of solutions to the nonhomogeneous quasilinear Kirchhoff- Schr\"{o}dinger-Poisson system with $ p $-Laplacian:
\begin{equation*}\label{1ip}
\begin{cases}\displaystyle
- \Big(a-b \int_{\mathbb{R}^3}|\nabla u|^p{\rm d}x \Big)\Delta_p u+|u|^{p-2}u+\lambda\phi_uu= |u|^{q-2}u+h(x), &\text{ }x\in \mathbb{R}^3,\\
-\Delta\phi=u^2, &\text{ }x\in \mathbb{R}^3,\\
\end{cases}
\end{equation*}
where $ a,b>0 $, $ \frac{4}{3} < p < \frac{12}{5} $, $ p < q < p^* =\frac{3p}{3-p} $, $ \lambda > 0 $. Under suitable assumptions on $ h(x) $, the existence of multiple solutions of the system is obtained by using the Ekeland variational principle and the Mountain pass theorem.
Key words: Kirchhoff-Schr\"odinger-Poisson system, $ p $-Laplacian, Ekeland variational principle, Mountain pass theorem
Wang Mei, Suo Hongmin, Zhang Xuemei, Wang Chenxi. Multiple Solutions for Nonhomogeneous Kirchhoff-Schrödinger-Poisson System with p-Laplacian[J]. Mathematical Theory and Applications, 2024, 44(2): 20-35.
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URL: http://mta.csu.edu.cn/EN/10.3969/j.issn.1006-8074.2024.02.002
http://mta.csu.edu.cn/EN/Y2024/V44/I2/20
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