On the logarithmic fractional Schrödinger–Poisson system with saddle-like potential
In this paper, we use variational methods to prove the existence of a positive solution for the following class of logarithmic fractional Schrödinger–Poisson system: \begin{equation*} \begin{cases} \epsilon^{2s}\left(-\Delta\right)^{s} u+V(x)u-\phi(x)u= u \log {u^{2}}&\quad\text{ in }\mathbb...
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| Language: | English |
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University of Szeged
2024-07-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10967 |
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| _version_ | 1846091029144403968 |
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| author | Huo Tao Lin Li |
| author_facet | Huo Tao Lin Li |
| author_sort | Huo Tao |
| collection | DOAJ |
| description | In this paper, we use variational methods to prove the existence of a positive solution for the following class of logarithmic fractional Schrödinger–Poisson system:
\begin{equation*}
\begin{cases}
\epsilon^{2s}\left(-\Delta\right)^{s} u+V(x)u-\phi(x)u= u \log {u^{2}}&\quad\text{ in }\mathbb{R}^{3}, \\
\epsilon^{2t}\left(-\Delta\right)^{t}\phi=|u|^{2}&\quad\text{ in }\mathbb{R}^{3},
\end{cases}
\end{equation*}
where $\epsilon>0$, $s,t\in(0,1)$, $\left(-\Delta\right)^{\alpha}$ is the fractional Laplacian and $V$ is a saddle-like potential. |
| format | Article |
| id | doaj-art-a24e3a6c867f4c31bff390c0a2837029 |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-a24e3a6c867f4c31bff390c0a28370292025-01-15T21:24:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-07-0120243612310.14232/ejqtde.2024.1.3610967On the logarithmic fractional Schrödinger–Poisson system with saddle-like potentialHuo Tao0https://orcid.org/0000-0002-1121-1351Lin LiChongqing Technology and Business University, Chongqing, ChinaIn this paper, we use variational methods to prove the existence of a positive solution for the following class of logarithmic fractional Schrödinger–Poisson system: \begin{equation*} \begin{cases} \epsilon^{2s}\left(-\Delta\right)^{s} u+V(x)u-\phi(x)u= u \log {u^{2}}&\quad\text{ in }\mathbb{R}^{3}, \\ \epsilon^{2t}\left(-\Delta\right)^{t}\phi=|u|^{2}&\quad\text{ in }\mathbb{R}^{3}, \end{cases} \end{equation*} where $\epsilon>0$, $s,t\in(0,1)$, $\left(-\Delta\right)^{\alpha}$ is the fractional Laplacian and $V$ is a saddle-like potential.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10967fractional schrödinger–poisson systemlogarithmic nonlinearityvariational methods |
| spellingShingle | Huo Tao Lin Li On the logarithmic fractional Schrödinger–Poisson system with saddle-like potential Electronic Journal of Qualitative Theory of Differential Equations fractional schrödinger–poisson system logarithmic nonlinearity variational methods |
| title | On the logarithmic fractional Schrödinger–Poisson system with saddle-like potential |
| title_full | On the logarithmic fractional Schrödinger–Poisson system with saddle-like potential |
| title_fullStr | On the logarithmic fractional Schrödinger–Poisson system with saddle-like potential |
| title_full_unstemmed | On the logarithmic fractional Schrödinger–Poisson system with saddle-like potential |
| title_short | On the logarithmic fractional Schrödinger–Poisson system with saddle-like potential |
| title_sort | on the logarithmic fractional schrodinger poisson system with saddle like potential |
| topic | fractional schrödinger–poisson system logarithmic nonlinearity variational methods |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10967 |
| work_keys_str_mv | AT huotao onthelogarithmicfractionalschrodingerpoissonsystemwithsaddlelikepotential AT linli onthelogarithmicfractionalschrodingerpoissonsystemwithsaddlelikepotential |