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

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Abstract

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 Δu +c(x)u =f(x,u), with zero Dirichlet boundary conditions on the Sierpiski gasket. Our existence results do not require any growth conditions off(x, t) in t, in contrast to the classical theory of elliptic equations on smooth domains.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China

    Jiaxin Hu

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  1. Jiaxin Hu
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Correspondence to Jiaxin Hu.

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Hu, J. Multiple solutions for a class of nonlinear elliptic equations on the Sierpiński gasket. Sci. China Ser. A-Math. 47, 772 (2004). https://doi.org/10.1360/02ys0366

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  • DOI: https://doi.org/10.1360/02ys0366

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