20.500.12556/RUL-137708 Degenerate fractional Kirchhoff-type system with magnetic fields and upper critical growth This paper deals with the following degenerate fractional Kirchhoff-type system with magnetic fields and critical growth: ▫$$\begin{aligned} \left\{ \begin{array}{lll} -\mathfrak{M}(\Vert u\Vert _{s,A}^2)[(-\Delta )^s_Au+u] = G_u(|x|,|u|^2,|v|^2) \\ \quad +\left( \mathcal{I}_\mu *|u|^{p^*}\right) |u|^{p^*-2}u \ &{}\text{ in }\,\,\mathbb {R}^N,\\ \mathfrak{M}(\Vert v\Vert _{s,A})[(-\Delta )^s_Av+v] = G_v(|x|,|u|^2,|v|^2) \\ \quad +\left( \mathcal{I}_\mu *|v|^{p^*}\right) |v|^{p^*-2}v \ &{}\text{ in }\,\,\mathbb{R}^N, \end{array}\right. \end{aligned}$$▫ where ▫$$\begin{aligned}\Vert u\Vert _{s,A}=\left( \iint _{\mathbb{R}^{2N}}\frac{|u(x)-e^{i(x-y)\cdot A(\frac{x+y}{2})}u(y)|^2}{|x-y|^{N+2s}}{\text{d}}x {\text{d}}y+\int _{\mathbb{R}^N}|u|^2{\text {d}}x\right) ^{1/2},\end{aligned}$$▫ and ▫$(-\Delta )_{A}^s$▫ and ▫$A$▫ are called magnetic operator and magnetic potential, respectively, ▫$\mathfrak{M}: \mathbb{R}^{+}_{0}\rightarrow \mathbb{R}^{+}_0$▫ is a continuous Kirchhoff function, ▫$\mathcal{I}_\mu (x) = |x|^{N-\mu }$▫ with ▫$0<\mu <N$▫-function ▫$G$▫ satisfies some suitable conditions, and ▫$p^* =\frac{N+\mu }{N-2s}$▫. We prove the multiplicity results for this problem using the limit index theory. The novelty of our work is the appearance of convolution terms and critical nonlinearities. To overcome the difficulty caused by degenerate Kirchhoff function and critical nonlinearity, we introduce several analytical tools and the fractional version concentration-compactness principles which are useful tools for proving the compactness condition. fractional Kirchhoff-type system upper critical exponent concentration-compactness principle variational method multiple solutions true false true Angleški jezik Ni določen Članek v reviji 2022-06-29 07:59:15 2022-06-29 07:59:21 2022-09-15 04:15:42 0000-00-00 00:00:00 2022 0 0 23 str. iss. 4, art. 170 Vol. 19 Aug. 2022 0000-00-00 PostprintKoncna NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2022-08-01 2023-08-01 517.956 1660-5446 10.1007/s00009-022-02076-5 112532995 RAZ_Sun_Mingzhe_2022.pdf RAZ_Sun_Mingzhe_2022.pdf 1 A92194D8932F25A1134588843604755B 5b5b3d4233ad4086ccf60f32811df53ac9ac77fe3ef4efa6ef0a23b2fc32ff1a aea04cef-f770-11ec-8aca-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=157755 https://link.springer.com/article/10.1007/s00009-022-02076-5 1 6b049e6e-f770-11ec-8aca-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=157754 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0