20.500.12556/RUL-120370 Multiplicity of solutions for a class of fractional ▫$p(x, \cdot)$▫-Kirchhoff-type problems without the Ambrosetti-Rabinowitz condition 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}$▫ are continuous functions. Using variational methods, especially the symmetric mountain pass theorem due to Bartolo-Benci-Fortunato (Nonlinear Anal. 7(9):981-1012, 1983), we establish the existence of infinitely many solutions for this problem without assuming the Ambrosetti-Rabinowitz condition. Our main result in several directions extends previous ones which have recently appeared in the literature. fractional ▫$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 true false true Angleški jezik Ni določen Članek v reviji 2020-09-18 13:39:06 2020-09-18 13:39:10 2022-09-01 03:58:39 0000-00-00 00:00:00 2020 0 0 art. 150, str. 1-16 iss. 1 Vol. 2020 Dec. 2020 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.956 1687-2770 10.1186/s13661-020-01447-9 28792835 62113025 RAZ_Hamdani_Mohamed_Karim_2020.pdf RAZ_Hamdani_Mohamed_Karim_2020.pdf 1 268B0C8A2511D42DFADC4892B395FF0B 21adfd15b818de8d4f12c82387f7e828c5da9199418a396774596f4c3bbf905a 120b8d64-a1ba-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=135160 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0