Degenerate fractional Kirchhoff-type system with magnetic fields and upper critical growth

Mingzhe Sun (Author), Shaoyun Shi (Author), Dušan Repovš (Author)

Abstract

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

Keywords

fractional Kirchhoff-type system;upper critical exponent;concentration-compactness principle;variational method;multiple solutions;

Data

Language:	English
Year of publishing:	2022
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	517.956
COBISS:	112532995
ISSN:	1660-5446
Views:	50
Downloads:	10
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Embargo end date (OpenAIRE):	2023-08-01
Pages:	art. 170 (23 str.)
Volume:	ǂVol. ǂ19
Issue:	ǂiss. ǂ4
Chronology:	Aug. 2022
DOI:	10.1007/s00009-022-02076-5
ID:	15776717