Nonlinear problems on the Sierpiński gasket

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

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].

• Language: English
• Keywords: Sierpiński gasket, fractal domains, nonlinear elliptic equation, weak Laplacian
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2017
• Number of pages: Str. 883-895
• Numbering: Vol. 452, iss. 2
• PID: 20.500.12556/RUL-109898
• UDC: 517.95
• ISSN on article: 0022-247X
• DOI: 10.1016/j.jmaa.2017.03.032
• COBISS.SI-ID: 17994841
• Publication date in RUL: 10.09.2019