Full-Text Search:
Home|Journal Papers|About CNKI|User Service|FAQ|Contact Us|中文
《中国科学A辑(英文版)》 2004-05
Add to Favorite Get Latest Update

Multiple solutions for a class of nonlinear elliptic equations on the Sierpinski gasket

HU Jiaxin Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China  
This paper investigates a class of nonlinear elliptic equations on a fractal domain. We establish a strong Sobolev-type inequality which leads to the existence of multiple non-trivial solutions of △u+ c(x)u = f(x, u), with zero Dirichlet boundary conditions on the Sierpihski gasket. Our existence results do not require any growth conditions of f(x,t) in t, in contrast to the classical theory of elliptic equations on smooth domains.
【Key Words】: Sierpinski gasket energy form Laplacian operator eigenvalue problem genus weak solution.
【CateGory Index】: O177
Download(CAJ format) Download(PDF format)
CAJViewer7.0 supports all the CNKI file formats; AdobeReader only supports the PDF format.
【Co-citations】
Chinese Journal Full-text Database 7 Hits
1 Mao Yonghua (Department of Mathematics, Beijing Normal University, 100875, Beijing, China);LOGARITHMIC SOBOLEV INEQUALITY ON CANTOR SETS[J];JOURNAL OF BEIJING NORMAL UNIVERSITY(NATURAL SCIENCE);1999-02
2 YAN Kun(Xi'an Modern Nonlinear Science Applying Institute,Xi'an 710061,China);Introduction on background medium theory about celestial body motion orbit and foundation of fractional-dimension calculus about self-fractal measure calculation[J];Progress in Geophysics;2007-02
3 HU JIAXINDepartment of Mathematics, Tsinghua University, Beijing 100084, China.;THE NAGUMO EQUATION ON SELF-SIMILAR FRACTAL SETS[J];数学年刊B辑(英文版);2002-04
4 Chen Hua He Zhenya School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China;SEMILINEAR ELLIPTIC EQUATIONS ON FRACTAL SETS[J];数学物理学报(英文版);2009-02
5 Chen Hua (Department of Mathematics, Wuhan University, Wuhan 430072, China) (Email: chenhua @ whu. edu. cn)Sleeman Brian D.(School of Mathematics, University of Leeds, Leeds LS29JT, England, UK) (Email: bds @ amsta. leeds. ac. uk);Counting Function Asymptotics and the Weak Weyl-Berry Conjecture for Connected Domains with Fractal Boundaries[J];ACTA MATHEMATICA SINICA;1998-06
6 HE Zhen-ya (School of Math and Statistics,Wuhan University,Wuhan 430072,China);NON-LINEAR PARABOLIC EQUATIONS ON SELF-SIMILAR FRACTAL SETS[J];Journal of Mathematics;2010-01
7 HE Zhenya,CHEN Hua School of Mathematics and Statistics,Wuhan University,Wuhan 430072,Hubei,China;Non-Linear Elliptic Equations on Fractal Domain[J];武汉大学自然科学学报(英文版);2007-03
©2006 Tsinghua Tongfang Knowledge Network Technology Co., Ltd.(Beijing)(TTKN) All rights reserved