Multiple Solutions of Dirichlet Problems on the Sierpinski Gasket

被引：8
|
作者：
Breckner, Brigitte E. [1 ]
Varga, Csaba [1 ]
机构：
[1] Univ Babes Bolyai, Fac Math & Comp Sci, Cluj Napoca 400084, Romania
来源：
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2015年 / 167卷 / 03期
关键词：
Sierpinski gasket; Weak Laplacian; Dirichlet problem on the Sierpinski gasket; Weak solution; Critical point; LINKING TYPE SOLUTIONS; MOUNTAIN PASS; PRINCIPLE; EQUATIONS;
D O I：
10.1007/s10957-013-0368-7
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
There are treated nonlinear, elliptic, and parameter-depending problems, defined on the Sierpinski gasket, a highly non-smooth fractal set. Even if the structure of this fractal differs considerably from that of (open) domains of Euclidean spaces, the paper emphasizes that PDEs defined on it may be studied (as in the Euclidean case) by means of certain variational methods. Using such methods, and some recent abstract multiplicity theorems by B. Ricceri, there are proved several results concerning the existence of multiple solutions of three-parameter Dirichlet problems defined on the Sierpinski gasket.
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页码：842 / 861
页数：20
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