On the existence of three solutions for the Dirichlet problem on the Sierpinski gasket

被引：27

作者：

Breckner, Brigitte E. ^{[1
]}

Repovs, Dusan ^{[2
]}

Varga, Csaba ^{[1
]}

机构：

[1] Univ Babes Bolyai, Fac Math & Comp Sci, Cluj Napoca 400084, Romania

[2] Inst Math Phys & Mech, SI-1001 Ljubljana, Slovenia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 09期

关键词：

Sierpinski gasket; Weak Laplacian; Dirichlet problem on the Sierpinski gasket; Weak solution; Critical point; Minimax theorems; Mountain pass theorems; CRITICAL-POINTS THEOREM; NONLINEAR ELLIPTIC-EQUATIONS; FRACTALS;

D O I：

10.1016/j.na.2010.06.064

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We apply a recently obtained three-critical-point theorem of B. Ricceri to prove the existence of at least three solutions of certain two-parameter Dirichlet problems defined on the Sierpinski gasket. We also show the existence of at least three nonzero solutions of certain perturbed two-parameter Dirichlet problems on the Sierpinski gasket, using both the mountain pass theorem of Ambrosetti and Rabinowitz and that of Pucci and Serrin. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：2980 / 2990

页数：11

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