Nonlinear problems on the Sierpiński gasket

Molica Bisci, Giovanni (avtor), Repovš, Dušan (avtor), Servadei, Raffaella (avtor)

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].

• Jezik: Angleški jezik
• Ključne besede: Sierpiński gasket, fractal domains, nonlinear elliptic equation, weak Laplacian
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2017
• Št. strani: Str. 883-895
• Številčenje: Vol. 452, iss. 2
• PID: 20.500.12556/RUL-109898
• UDK: 517.95
• ISSN pri članku: 0022-247X
• DOI: 10.1016/j.jmaa.2017.03.032
• COBISS.SI-ID: 17994841
• Datum objave v RUL: 10.09.2019