Multiplicity of solutions for a class of fractional p(x, [cdot])-Kirchhoff-type problems without the Ambrosetti-Rabinowitz condition

Mohamed Karim Hamdani (Avtor), Jiabin Zuo (Avtor), Nguyen Thanh Chung (Avtor), Dušan Repovš (Avtor)

Povzetek

We are interested in the existence of solutions for the following fractional ▫$p(x,\cdot)$▫-Kirchhoff-type problem: ▫$$\textstyle\begin{cases} M ( \int _{\Omega \times \Omega } {\frac{ \vert u(x)-u(y) \vert ^{p(x,y)}}{p(x,y) \vert x-y \vert ^{N+p(x,y)s}}} \,dx \,dy )(-\Delta )^{s}_{p(x,\cdot )}u = f(x,u), \quad x\in \Omega , \\ u= 0, \quad x\in \partial \Omega , \end{cases}$$▫ where ▫$\Omega \subset \mathbb{R}^{N}$▫,▫$ N\geq 2$▫ is a bounded smooth domain, ▫$s\in (0,1)$▫, ▫$p: \overline{\Omega }\times \overline{\Omega } \rightarrow (1, \infty )$▫, ▫$(-\Delta )^{s}_{p(x,\cdot)}$▫ denotes the ▫$p(x,\cdot )$▫-fractional Laplace operator, ▫$M: [0,\infty ) \to [0, \infty )$▫, and ▫$f: \Omega \times \mathbb{R} \to \mathbb{R}$▫ are continuous functions. Using variational methods, especially the symmetric mountain pass theorem due to Bartolo-Benci-Fortunato (Nonlinear Anal. 7(9):981-1012, 1983), we establish the existence of infinitely many solutions for this problem without assuming the Ambrosetti-Rabinowitz condition. Our main result in several directions extends previous ones which have recently appeared in the literature.

Ključne besede

fractional ▫$p(x,\cdot)$▫-Kirchhoff-type problems;▫$p(x,\cdot)$▫-fractional Laplace operator;Ambrosetti-Rabinowitz type conditions;symmetric mountain pass theorem;Cerami compactness condition;fractional Sobolev spaces with variable exponent;multiplicity of solutions;

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:	28792835
ISSN:	1687-2770
Št. ogledov:	418
Št. prenosov:	122
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Vrsta dela (COBISS):	Članek v reviji
Strani:	art. 150, str. 1-16
Letnik:	ǂVol. ǂ2020
Zvezek:	ǂiss. ǂ1
Čas izdaje:	Dec. 2020
DOI:	10.1186/s13661-020-01447-9
ID:	12042780