INFINITELY MANY SOLUTIONS FOR THE DIRICHLET PROBLEM ON THE SIERPINSKI GASKET

被引：30
|
作者：
Breckner, Brigitte E. [1 ]
Radulescu, Vicentiu D. [2 ,3 ]
Varga, Csaba [1 ]
机构：
[1] Univ Babes Bolyai, Fac Math & Comp Sci, Cluj Napoca 400084, Romania
[2] Romanian Acad, Inst Math Simion Stoilow, Bucharest 010702, Romania
[3] Univ Craiova, Dept Math, Craiova 200585, Romania
来源：
ANALYSIS AND APPLICATIONS | 2011年 / 9卷 / 03期
关键词：
Sierpinski gasket; weak Laplace operator; nonlinear elliptic equation; weak solution; Hausdorff measure; attractor; NONLINEAR ELLIPTIC-EQUATIONS; DIFFERENTIAL-EQUATIONS;
D O I：
10.1142/S0219530511001844
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the nonlinear elliptic equation Delta u(x) + a(x) u(x) = g(x) f(u(x)) on the Sierpinski gasket and with zero Dirichlet boundary condition. By extending a method introduced by Faraci and Kristaly in the framework of Sobolev spaces to the case of function spaces on fractal domains, we establish the existence of infinitely many weak solutions.
引用
收藏
页码：235 / 248
页数：14
相关论文
共 50 条
  • [41] ACYCLIC ORIENTATIONS ON THE SIERPINSKI GASKET
    Chang, Shu-Chiuan
    INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2012, 26 (24):
  • [42] Extensions and their Minimizations on the Sierpinski Gasket
    Pak-Hin Li
    Nicholas Ryder
    Robert S. Strichartz
    Baris Evren Ugurcan
    Potential Analysis, 2014, 41 : 1167 - 1201
  • [43] Hausdorff measure of Sierpinski gasket
    Zuoling Zhou
    Science in China Series A: Mathematics, 1997, 40 : 1016 - 1021
  • [44] INFINITELY MANY SOLUTIONS FOR A PERTURBED NONLINEAR FRACTIONAL BOUNDARY-VALUE PROBLEM
    Bai, Chuanzhi
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2013,
  • [45] Existence and multiplicity of weak solutions for gradient-type systems with oscillatory nonlinearities on the Sierpinski gasket
    Alrikabi, Haiffa Muhsan B.
    Afrouzi, Ghasem A.
    Alimohammady, Mohsen
    HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2019, 48 (05): : 1461 - 1478
  • [46] Spanning Trees on the Sierpinski Gasket
    Shu-Chiuan Chang
    Lung-Chi Chen
    Wei-Shih Yang
    Journal of Statistical Physics, 2007, 126 : 649 - 667
  • [47] Dimer Coverings on the Sierpinski Gasket
    Shu-Chiuan Chang
    Lung-Chi Chen
    Journal of Statistical Physics, 2008, 131 : 631 - 650
  • [48] Box dimension of harmonic functions on higher dimensional Sierpinski gasket and Sierpinski gasket with bilateral energy
    Gopalakrishnan, Harsha
    Prasad, Srijanani Anurag
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 540 (01)
  • [49] On the packing measure of the Sierpinski gasket
    Llorente, Marta
    Eugenia Mera, M.
    Moran, Manuel
    NONLINEARITY, 2018, 31 (06) : 2571 - 2589
  • [50] Spanning forests on the Sierpinski gasket
    Chang, Shu-Chiuan
    Chen, Lung-Chi
    DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2008, 10 (02): : 55 - 76
12345