20.500.12556/RUL-109898 Nonlinear problems on the Sierpiński gasket This paper concerns with a class of elliptic equations on fractal domains depending on a real parameter. Our approach is based on variational methods. More precisely, the existence of at least two non-trivial weak (strong) solutions for the treated problem is obtained exploiting a local minimum theorem for differentiable functionals defined on reflexive Banach spaces. A special case of the main result improves a classical application of the Mountain Pass Theorem in the fractal setting, given by Falconer and Hu in [K. J. Falconer, J. Hu, Nonlinear elliptic equations on the Sierpiński gasket, J. Math. Anal. Appl. 240 (1999) 552-573]. Sierpiński gasket fractal domains nonlinear elliptic equation weak Laplacian true false true Angleški jezik Ni določen Članek v reviji 2019-09-10 08:01:40 2019-09-10 08:01:42 2022-08-22 03:40:22 0000-00-00 00:00:00 2017 0 0 Str. 883-895 iss. 2 Vol. 452 2017 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.95 0022-247X 10.1016/j.jmaa.2017.03.032 17994841 RAZ_Molica_Bisci_Giovanni_i2017.pdf RAZ_Molica_Bisci_Giovanni_i2017.pdf 1 82907D2119EB050A7F694E0916CC0E12 5c5287b2f092718e2461403dfcfb5d654ab16aa2a431f369e93784aeb9233191 fc1c463c-a1b6-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=121502 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0