On critical variable-order Kirchhoff type problems with variable singular exponent

Jiabin Zuo (Author), Debajyoti Choudhuri (Author), Dušan Repovš (Author)

Abstract

We establish a continuous embedding ▫$W^{s(\cdot),2}(\Omega) \hookrightarrow L^{\alpha (\cdot)}(\Omega)$▫, where the variable exponent ▫$\alpha(x)$▫ can be close to the critical exponent ▫$2_s^\ast = \frac{2N}{N-2\bar{s}(x)}$▫, with ▫$\bar{s}(x) = s(x,x)$▫ for all ▫$x \in \bar{\Omega}$▫. Subsequently, this continuous embedding is used to prove the multiplicity of solutions for critical nonlocal degenerate Kirchhoff problems with a variable singular exponent. Moreover, we also obtain the uniform ▫$L^\infty$▫-estimate of these infinite solutions by a bootstrap argument.

Keywords

fractional Laplacian of variable-order;continuous embedding;genus;symmetric mountain pass theorem;variable singular exponent;

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:	106082051
ISSN:	0022-247X
Views:	118
Downloads:	67
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	art. 126264 (18 str.)
Volume:	ǂVol. ǂ514
Issue:	ǂiss.ǂ1
Chronology:	Oct. 2022
DOI:	10.1016/j.jmaa.2022.126264
ID:	15209470