Nonlinear problems on the Sierpiński gasketMolica Bisci, Giovanni (Avtor) Repovš, Dušan (Avtor) Servadei, Raffaella (Avtor) Sierpiński gasketfractal domainsnonlinear elliptic equationweak LaplacianThis 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].20172019-09-10 08:01:40Članek v reviji109898UDK: 517.95ISSN pri članku: 0022-247XDOI: 10.1016/j.jmaa.2017.03.032COBISS_ID: 17994841sl