| Title: | On the $p$-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity |
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| Authors: | ID Zhao, Min (Author)
ID Song, Yueqiang (Author)
ID Repovš, Dušan (Author) |
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| Files: |  URL - Source URL, visit https://www.degruyter.com/document/doi/10.1515/dema-2023-0124/html
 PDF - Presentation file, download (2,62 MB)
MD5: ED9AA72BAA996D5DD3C56EB7D21FD1F1
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | In this article, we deal with the following $p$-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity: $ M\left([u]_{s,A}^{p}\right)(-\Delta)_{p, A}^{s} u+V(x)|u|^{p-2} u=\lambda\left(\int_\limits{\mathbb{R}^{N}} \frac{|u|^{p_{\mu, s}^{*}}}{|x-y|^{\mu}} \mathrm{d}y\right)|u|^{p_{\mu, s}^{*}-2} u+k|u|^{q-2}u,\ x \in \mathbb{R}^{N},$ where $0 < s < 1 < p$, $ps < N$, $p < q < 2p^{*}_{s,\mu}$, $0 < \mu < N$, $\lambda$ and $k$ are some positive parameters, $p^{*}_{s,\mu}=\frac{pN-p\frac{\mu}{2}}{N-ps}$ is the critical exponent with respect to the Hardy-Littlewood-Sobolev inequality, and functions $V$, $M$ satisfy the suitable conditions. By proving the compactness results using the fractional version of concentration compactness principle, we establish the existence of nontrivial solutions to this problem. |
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| Keywords: | Hardy-Littlewood-Sobolev nonlinearity, Schrödinger-Kirchhoff equations, variational methods, electromagnetic fields |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | 18 str. |
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| Numbering: | Vol. 57, iss. 1, article no. 20230124 |
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| PID: | 20.500.12556/DiRROS-18199  |
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| UDC: | 517.9 |
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| ISSN on article: | 2391-4661 |
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| DOI: | 10.1515/dema-2023-0124 |
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| COBISS.SI-ID: | 180796163 |
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| Note: |
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| Publication date in DiRROS: | 16.02.2024 |
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| Views: | 1055 |
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| Downloads: | 541 |
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