Fractional magnetic Schrödinger-Kirchhoff problems with convolution and critical nonlinearities

Sihua Liang (Avtor), Dušan Repovš (Avtor), Binlin Zhang (Avtor)

Povzetek

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 ▫$0 0$▫ 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.

Ključne besede

Choquard-type equation;critical nonlinearity;fractional magnetic operator;variational method;

Podatki

Jezik:	Angleški jezik
Leto izida:	2020
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	517.956
COBISS:	18870617
ISSN:	0170-4214
Št. ogledov:	468
Št. prenosov:	289
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Vrsta dela (COBISS):	Članek v reviji
Strani:	str. 2473-2490
Letnik:	ǂVol. ǂ43
Zvezek:	ǂiss. ǂ5
Čas izdaje:	March 2020
DOI:	10.1002/mma.6057
ID:	11763917