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

页码：235 / 248

页数：14

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