[1] Barlow M T, Bass R F. Transition deneities for Brownian motion on the Sierpinski carpet. Probab Theory Related Fields, 1992, 91: 307–330
[2] Birroli M, Mosco U. Sobolev and isoperimetric inequalities for Dirichlet forms on discontinuous media. Rend Mat Acc Lincei s, 1995, 96: 37–43
[3] Hambly B M. Brownian motion on a random recursive Sierpinski gasket. Ann Probab, 1997, 25: 1059–1102
[4] Kusuoka S, Yin Z X. Dirichlet forms on fractals: Poincare constant and Resistance. Probab Theory Related Fields, 1992, 93: 169–196
[5] Lapidus M L. Analysis on fractals,Laplacians on self-similar sets, noncommutative geometry and spectral dimensions. Topol Methods Nonlinear Anal, 1994, 4: 137–195
[6] Mosco U. Dirichlet forms and self-similarity. In: J Jost et al, eds. New directions in Dirichlet forms. Cambridge: International Press, 1998
[7] Barlow M T, Kigami J. Localized eigenfunctions of the Laplacian on p.c.f. self-similar sets. J London Math Soc, 1997, 56(2): 320[-332
[8] Falconer J K. Techniques in Fractal Geometry. Chi Chester: John Wiley, 1997
[9] Falconer J K. Fractal Geometry-Mathematical Foundations and Applications. Chi Chester: John wiley, 1992
[10] Kigami J. In quest of fractal analysis. In: Yamaguti M, Hata M, Kigami J, eds. Mathematics of Fractals, Providence, RI: American Mathematical Society, 1993. 53–73
[11] Kigami J. Harmonic calculus on p.c.f self-similar sets. Trans Am Math Soc, 1993, 335: 721–755
[12] Kigami J, Lapidus M L. Weyl’s problem for the spectral distribution of Laplacians on p.c.f. self-similar sets. Commun Math Phys, 1993, 158: 93–125
[13] Falconer J K. Semi linear PDES on self-similar fractals. Commun Math Phys, 1999, 206: 235–245
[14] Mosco U. Lagrangian metrics on fractals. Proc Symp Math, 1998, 54: 301–323
[15] Kigami J.Effective resistances for harmonic structures on p.c.f. self-similar sets. Math Proc Cambridge Pyilos Soc, 1994, 115: 291–303
[16] Ambrosetti A, Prodi G. A primer of Nonlinear Analysis. Cambridge University Press, 1992
[17] Ambrosetti A, Rabinowitz G. Dual variational methods in critical point theory and applications. J Funct Anal, 1973, 14: 349–381
[18] Chow S N, Hale J K. Methods of Bifurcation Theory. Berlin: Springer, 1982
[19] Lions P L. On the existence of positive solutions of semi-linear elliptic equations. SIAM Review, 1982, 24:441–467
[20] Strichartz R S. Some properties of laplacians on fractals. J Funct Anal, 2000, 174: 76–127
[21] Lindqvist P. On the equation div (|∇|p−2∇u) + |u|p−2u = 0. Proc AMS, 1990, 109: 157–164
[22] Posta G. Spectral asymptotics for variational fractals. Z Anal Anwendungen, 1998, 17: 417–430
[23] Li G B, Zhou H S. Dirichlet problem of P-Laplacian with nonlinear term f(x, u) ∼ up−1 at infinity. In:
Brezis H, Li, Liu J Q, Rabionowitz P H, eds. Morse Theory, Minimax Theory and Their Applications to Nonlinear Differential Equations. International Press |