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

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

Povzetek

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.

Ključne besede

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

Podatki

Jezik:	Angleški jezik
Leto izida:	2022
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	517.956
COBISS:	106082051
ISSN:	0022-247X
Št. ogledov:	118
Št. prenosov:	67
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Vrsta dela (COBISS):	Članek v reviji
Strani:	art. 126264 (18 str.)
Letnik:	ǂVol. ǂ514
Zvezek:	ǂiss.ǂ1
Čas izdaje:	Oct. 2022
DOI:	10.1016/j.jmaa.2022.126264
ID:	15209470