期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 452, 期 2, 页码 883-895出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2017.03.032
关键词
Sierpinski gasket; Fractal domains; Nonlinear elliptic equation; Weak Laplacian
资金
- INdAM-GNAMPA
- DiSBeF Research Project
- DiSPeA Research Project
- PRIN [2015KB9WPT_009]
- FP7-IDEAS-ERC Starting Grant [2011 077749 EPSILON]
- Slovenian Research Agency [P1-0292-0101]
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 [14]. (C) 2017 Elsevier Inc. All rights reserved.
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