20.500.12556/RUL-116616 Fractional magnetic Schrödinger-Kirchhoff problems with convolution and critical nonlinearities In this paper, we are concerned with the existence and multiplicity of solutions for the fractional Choquard-type Schrödinger-Kirchhoff equations with electromagnetic fields and critical nonlinearity: ▫$$\begin{cases} \varepsilon^{2s} N([u]^2_{s,A}) (-\Delta)^s_A u + V(x)u = (|x|^{-\alpha} \ast F(|u|^2)) f(|u|^2)u + |u|^{2^\ast_s-2}u, & x\in \mathbb{R}^N, \\ U(x) \to 0, & \text{as} \quad |x| \to \infty, \end{cases}$$▫ where ▫$(-\Delta)^s_A$▫ is the fractional magnetic operator with ▫$0<s<1$▫, ▫$2^\ast_s = 2N/(N-2s)$▫, ▫$\alpha < \min\{N, 4s\}$▫, ▫$M \colon \mathbb{R}^+_0 \to \mathbb{R}^+_0$▫ is a continuous function, ▫$A\colon \mathbb{R}^N \to \mathbb{R}^N$▫ is the magnetic potential, ▫$F(|u|) =\int^{|u|}_0f(t)dt$▫, and ▫$\varepsilon > 0$▫ is a positive parameter. The electric potential ▫$V \in C(\mathbb{R}^N, \mathbb{R}^+_0)$▫ satisfies ▫$V(x)=0$▫ in some region of ▫$\mathbb{R}^N$▫, which means that this is the critical frequency case. We first prove the ▫$(PS)_c$▫ condition, by using the fractional version of the concentration compactness principle. Then, applying also the mountain pass theorem and the genus theory, we obtain the existence and multiplicity of semiclassical states for the above problem. The main feature of our problems is that the Kirchhoff term ▫$M$▫ can vanish at zero. Choquard-type equation critical nonlinearity fractional magnetic operator variational method true false true Angleški jezik Ni določen Članek v reviji 2020-05-29 13:42:46 2020-05-29 13:42:49 2022-08-28 03:50:16 0000-00-00 00:00:00 2020 0 0 Str. 2473-2490 iss. 5 Vol. 43 March 2020 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.956 0170-4214 10.1002/mma.6057 18870617 25911808 RAZ_Liang_Sihua_2020.pdf RAZ_Liang_Sihua_2020.pdf 1 BE50E2AE3837BA34284AB891514D429C 0bc8fc378c9f665505da304f1e739eaa19a16984b408b22cbaf3bdd27b5a4caf f961a553-a1b8-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=130255 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0