AN APPLICATION OF A FIXED-POINT THEOREM TO NEUMANN PROBLEMS ON THE SIERPINSKI FRACTAL

被引：0

作者：

Breckner, Brigitte E. ^{[1
]}

Varga, Csaba ^{[1
]}

机构：

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

来源：

FIXED POINT THEORY | 2018年 / 19卷 / 02期

关键词：

Sierpinski gasket; harmonic extension procedure; Leray-Schauder continuation principle; Neumann problem on the Sierpinski gasket;

D O I：

10.24193/fpt-ro.2018.2.38

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prepare first the background for the study of Neumann problems on the Sierpinski fractal in the N-dimensional Euclidean space. Hereafter we apply the Leray-Schauder continuation principle to prove the existence of at least one solution of certain Neumann problems on this fractal.

引用

页码：475 / 486

页数：12

共 11 条

[1]

Bauer H., 2001, DEGRUYTER STUDIES MA, V26

[2]

Breckner B. E., 2013, MATHEMATICA, V55, P142

[3]

Breckner B. E., 2014, SPRINGER OPTIM APPL, V94, P119

[4] The Laplace operator on the Sierpinski gasket with Robin boundary conditions [J].

Breckner, Brigitte E. ;

Chill, Ralph .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2017, 38 :245-260

[5] Non-linear elliptical equations on the Sierpinski gasket [J].

Falconer, KJ ;

Hu, JX .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 240 (02) :552-573

[6] HARMONIC CALCULUS ON PCF SELF-SIMILAR SETS [J].

KIGAMI, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 335 (02) :721-755

[7]

Kigami J., 1989, Jpn. J. Appl. Math., V6, P259, DOI [10.1007/hf03167882, DOI 10.1007/HF03167882]

[8]

Kigami J., 2001, ANAL FRACTALS

[9]

O'Regan D., 2001, THEOREMS LERAY SCHAD

[10]

Strichartz R. S., 2006, DIFFERENTIAL EQUATIO

← 1 2 →