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.
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页码：235 / 248
页数：14
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