20.500.12556/RUL-113866 Existence of solutions for systems arising in electromagnetism In this paper, we study the following ▫$p(x)$▫-curl systems: ▫$$\begin{cases} \nabla \times (|\nabla \times \mathbf{u}|^{p(x)-2}\nabla \times \mathbf{u}) + a(x)|\mathbf{u}|^{p(x)-2}\mathbf{u} = \lambda f(x, \mathbf{u}) + \mu g(x, \mathbf{u}), \quad \nabla \cdot \mathbf{u} & \text{in} \; \Omega, \\ |\nabla \times \mathbf{u}|^{p(x)-2}\nabla \times \mathbf{u} \times \mathbf{n} = 0, \quad \mathbf{u} \cdot \mathbf{n} = 0 & \text{on} \; \partial\Omega, \end{cases}$$▫ where ▫$\Omega \subset \mathbb{R}^3$▫ is a bounded simply connected domain with a ▫$C^{1,1}$▫-boundary, denoted by ▫$\delta\Omega$▫, ▫$p \colon \overline{\Omega} \to (1, +\infty)$▫ is a continuous function, ▫$a \in L^\infty(\Omega$▫, ▫$f, g \colon \Omega \times \mathbb{R}^3 \to \mathbb{R}^3$▫ are Carathéodory functions, and ▫$\lambda, \mu$▫ are two parameters. Using variational arguments based on Fountain theorem and Dual Fountain theorem, we establish some existence and non-existence results for solutions of this problem. Our main results generalize the results of Xiang, Wang and Zhang (J. Math. Anal. Appl., 2016), Bahrouni and Repovš (Complex Var. Elliptic Equ., 2018), and Bin and Fang (Mediterr. J. Math., 2019). variable exponent p(x)-curl system Palais Smale compactness condition Fountain theorem Dual Fountain theorem existence of solutions multiplicity of solutions electromagnetism true false true Angleški jezik Ni določen Članek v reviji 2020-02-10 08:11:04 2020-02-10 08:11:08 2022-08-26 03:47:51 0000-00-00 00:00:00 2020 0 0 art. 123898 [18 str.] iss.2 Vol. 486 June 2020 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.956.2 0022-247X 10.1016/j.jmaa.2020.123898 18900057 RAZ_Hamdani_Mohamed_Karim_2020.pdf RAZ_Hamdani_Mohamed_Karim_2020.pdf 1 AE50F9055C106E6B66AE2CCA48F4419B e7c45d274da5628d9d6e0d8d4ecbcab156d548700c573d2753cf02541d676127 2bc92d3e-a1b8-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=125977 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0