Free Access
Issue
ESAIM: COCV
Volume 18, Number 4, October-December 2012
Page(s) 941 - 953
DOI https://doi.org/10.1051/cocv/2011199
Published online 16 January 2012
  1. S. Alexander, Some properties of the spectrum of the Sierpiński gasket in a magnetic field. Phys. Rev. B 29 (1984) 5504–5508. [CrossRef] [MathSciNet] [Google Scholar]
  2. G. Bonanno and R. Livrea, Multiplicity theorems for the Dirichlet problem involving the p-Laplacian. Nonlinear Anal. 54 (2003) 1–7. [CrossRef] [MathSciNet] [Google Scholar]
  3. G. Bonanno and G. Molica Bisci, Infinitely many solutions for a boundary value problem with discontinuous nonlinearities. Bound. Value Probl. 2009 (2009) 1–20. [CrossRef] [Google Scholar]
  4. G. Bonanno and G. Molica Bisci, Infinitely many solutions for a Dirichlet problem involving the p-Laplacian. Proc. R. Soc. Edinb. Sect. A 140 (2010) 737–752. [CrossRef] [Google Scholar]
  5. G. Bonanno, G. Molica Bisci and D. O’Regan, Infinitely many weak solutions for a class of quasilinear elliptic systems. Math. Comput. Model. 52 (2010) 152–160. [CrossRef] [Google Scholar]
  6. B.E. Breckner, D. Repovš and Cs. Varga, On the existence of three solutions for the Dirichlet problem on the Sierpiński gasket. Nonlinear Anal. 73 (2010) 2980–2990. [CrossRef] [MathSciNet] [Google Scholar]
  7. B.E. Breckner, V. Rădulescu and Cs. Varga, Infinitely many solutions for the Dirichlet problem on the Sierpiński gasket. Analysis and Applications 9 (2011) 235–248. [CrossRef] [MathSciNet] [Google Scholar]
  8. G. D’Aguì and G. Molica Bisci, Infinitely many solutions for perturbed hemivariational inequalities. Bound. Value Probl. 2011 (2011) 1–19. [Google Scholar]
  9. G. D’Aguì and G. Molica Bisci, Existence results for an Elliptic Dirichlet problem, Le Matematiche LXVI, Fasc. I (2011) 133–141. [Google Scholar]
  10. K.J. Falconer, Semilinear PDEs on self-similar fractals. Commun. Math. Phys. 206 (1999) 235–245. [CrossRef] [Google Scholar]
  11. K.J. Falconer, Fractal Geometry : Mathematical Foundations and Applications, 2nd edition. John Wiley & Sons (2003). [Google Scholar]
  12. K.J. Falconer and J. Hu, Nonlinear elliptical equations on the Sierpiński gasket. J. Math. Anal. Appl. 240 (1999) 552–573. [CrossRef] [Google Scholar]
  13. M. Fukushima and T. Shima, On a spectral analysis for the Sierpiński gasket. Potential Anal. 1 (1992) 1–35. [CrossRef] [MathSciNet] [Google Scholar]
  14. S. Goldstein, Random walks and diffusions on fractals, in Percolation Theory and Ergodic Theory of Infinite Particle Systems, IMA Math. Appl. 8, edited by H. Kesten. Springer, New York (1987) 121–129. [Google Scholar]
  15. J. Hu, Multiple solutions for a class of nonlinear elliptic equations on the Sierpiński gasket. Sci. China Ser. A 47 (2004) 772–786. [CrossRef] [MathSciNet] [Google Scholar]
  16. C. Hua and H. Zhenya, Semilinear elliptic equations on fractal sets. Acta Mathematica Scientica 29 B (2009) 232–242. [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Kristály and G. Moroşanu, New competition phenomena in Dirichlet problems. J. Math. Pures Appl. 94 (2010) 555–570. [CrossRef] [Google Scholar]
  18. A. Kristály, V. Rădulescu and C. Varga, Variational Principles in Mathematical Physics, Geometry, and Economics : Qualitative Analysis of Nonlinear Equations and Unilateral Problems. Cambridge University Press, Cambridge (2010). [Google Scholar]
  19. J. Kigami, Analysis on Fractals. Cambridge University Press, Cambridge (2001). [Google Scholar]
  20. S. Kusuoka, A diffusion process on a fractal. Probabilistic Methods in Mathematical Physics, Katata/Kyoto (1985) 251–274; Academic Press, Boston, MA (1987). [Google Scholar]
  21. B.B. Mandelbrot, How long is the coast of Britain? Statistical self-similarity and fractional dimension, Science 156 (1967) 636–638. [CrossRef] [PubMed] [Google Scholar]
  22. B.B. Mandelbrot, Fractals : Form, Chance and Dimension. W.H. Freeman & Co., San Francisco (1977). [Google Scholar]
  23. B.B. Mandelbrot, The Fractal Geometry of Nature. W.H. Freeman & Co., San Francisco (1982). [Google Scholar]
  24. P. Omari and F. Zanolin, Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential. Comm. Partial Differential Equations 21 (1996) 721–733. [CrossRef] [MathSciNet] [Google Scholar]
  25. P. Omari and F. Zanolin, An elliptic problem with arbitrarily small positive solutions, Proceedings of the Conference on Nonlinear Differential Equations (Coral Gables, FL, 1999). Electron. J. Differ. Equ. Conf. 5. Southwest Texas State Univ., San Marcos, TX (2000) 301–308. [Google Scholar]
  26. R. Rammal, A spectrum of harmonic excitations on fractals. J. Phys. Lett. 45 (1984) 191–206. [CrossRef] [EDP Sciences] [Google Scholar]
  27. R. Rammal and G. Toulouse, Random walks on fractal structures and percolation clusters. J. Phys. Lett. 44 (1983) L13–L22. [CrossRef] [EDP Sciences] [Google Scholar]
  28. B. Ricceri, A general variational principle and some of its applications. J. Comput. Appl. Math. 113 (2000) 401–410. [CrossRef] [Google Scholar]
  29. W. Sierpiński, Sur une courbe dont tout point est un point de ramification. Comptes Rendus (Paris) 160 (1915) 302–305. [Google Scholar]
  30. R.S. Strichartz, Analysis on fractals. Notices Amer. Math. Soc. 46 (1999) 1199–1208. [MathSciNet] [Google Scholar]
  31. R.S. Strichartz, Solvability for differential equations on fractals. J. Anal. Math. 96 (2005) 247–267. [CrossRef] [MathSciNet] [Google Scholar]
  32. R.S. Strichartz, Differential Equations on Fractals, A Tutorial. Princeton University Press, Princeton, NJ (2006). [Google Scholar]

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