Nonlinear problems on the Sierpiński gasket

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

Abstract

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].

Keywords

Sierpiński gasket;fractal domains;nonlinear elliptic equation;weak Laplacian;

Data

Language:	English
Year of publishing:	2017
Typology:	1.01 - Original Scientific Article
Organization:	UL PEF - Faculty of Education
UDC:	517.95
COBISS:	17994841
ISSN:	0022-247X
Views:	509
Downloads:	319
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	str. 883-895
Volume:	ǂVol. ǂ452
Issue:	ǂiss. ǂ2
Chronology:	2017
DOI:	10.1016/j.jmaa.2017.03.032
ID:	11220308