Multiplicity of solutions for a class of fractional ▫$p(x, \cdot)$▫-Kirchhoff-type problems without the Ambrosetti-Rabinowitz conditionHamdani, Mohamed Karim (Avtor) Zuo, Jiabin (Avtor) Chung, Nguyen Thanh (Avtor) Repovš, Dušan (Avtor) fractional ▫$p(x\cdot)$▫-Kirchhoff-type problems▫$p(x\cdot)$▫-fractional Laplace operatorAmbrosetti-Rabinowitz type conditionssymmetric mountain pass theoremCerami compactness conditionfractional Sobolev spaces with variable exponentmultiplicity of solutionsWe 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.20202020-09-18 13:39:06Članek v reviji120370UDK: 517.956ISSN pri članku: 1687-2770DOI: 10.1186/s13661-020-01447-9COBISS_ID: 28792835OceCobissID: 62113025sl