On the $p$-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearityZhao, Min (Avtor) Song, Yueqiang (Avtor) Repovš, Dušan (Avtor) Hardy-Littlewood-Sobolev nonlinearitySchrödinger-Kirchhoff equationsvariational methodselectromagnetic fieldsIn 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.20242024-02-16 13:28:26Neznano18199sl