20.500.12556/RUL-109278 Existence and multiplicity results for a new ▫$p(x)$▫-Kirchhoff problem In this work, we study the existence and multiplicity results for the following nonlocal-Kirchhoff problem: ▫$$\begin{cases} -\big(a-b \int_\Omega \frac{1}{p(x}|\nabla u|^{p(x)} dx \big) \; \text{div} (|\nabla u|^{p(x)-2} \nabla u) = \\ = \lambda |u|^{p(x)-2}u + g(x,u) & \text{in} \; \Omega \\ u=0 & \text{on} \; \partial \Omega \end{cases}$$▫ where ▫$a \ge b > 0$▫ are constants, ▫$\Omega \subset \mathbb{R}^N$▫ is a bounded smooth domain ▫$p \in C(\overline{\Omega})$▫, with ▫$N > p(x) > 1$▫, ▫$\lambda$▫ is a real parameter and ▫$g$▫ is a continuous function. The analysis developed in this paper proposes an approach based on the idea of considering a new nonlocal term which presents interesting difficulties. variable exponent nonlocal Kirchhoff equation p(x)-Laplacian operator Palais-Smale condition Mountain Pass theorem Fountain theorem true false true Angleški jezik Ni določen Članek v reviji 2019-08-29 08:19:09 2019-08-29 08:19:10 2022-08-21 03:41:06 0000-00-00 00:00:00 2020 0 0 art. 111598 ( 15 str.) Vol. 190 Jan. 2020 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.956 0362-546X 10.1016/j.na.2019.111598 18706265 26027520 RAZ_Hamdani_Mohamed_Karim_i2020.pdf RAZ_Hamdani_Mohamed_Karim_i2020.pdf 1 D7C2F5B65F82B25B4318C7A80A32A580 4a40e724c50f11f7e540ac4fd079eb0443fe33b591ca9d7a96ab78ac76a4f98b d2be9037-a1b6-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=120807 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0