20.500.12556/DiRROS-18199 On the $p$-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity 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. Hardy-Littlewood-Sobolev nonlinearity Schrödinger-Kirchhoff equations variational methods electromagnetic fields true false true Angleški jezik Ni določen Neznano 2024-02-16 13:28:26 2024-02-16 13:28:26 2024-02-19 13:37:15 0000-00-00 00:00:00 2024 0 0 18 str. iss. 1, article no. 20230124 Vol. 57 Jan. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2024-01-01 517.9 2391-4661 10.1515/dema-2023-0124 180796163 https://www.degruyter.com/document/doi/10.1515/dema-2023-0124/html 1 8344dfe4-ccbe-11ee-aa6e-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=24715 10.1515_dema-2023-0124-1.pdf 10.1515_dema-2023-0124-1.pdf 1 ED9AA72BAA996D5DD3C56EB7D21FD1F1 41fd2ef07ccdc245aedbbfe09e37dd3e19364e83f8954c8c513029aa31a5e97e 03e264ae-ccbf-11ee-aa6e-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=24716 Inštitut za matematiko, fiziko in mehaniko 0 0 0