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《中国科学A辑(英文版)》 2004-05
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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
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Chinese Journal Full-text Database 7 Hits
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