Sublinear Elliptic Equation on Fractal Domains

Sublinear Elliptic Equation on Fractal Domains

Year:    2011

Journal of Partial Differential Equations, Vol. 24 (2011), Iss. 2 : pp. 97–113

Abstract

This paper investigates sub-linear elliptic equations on self-similar fractal sets. With an appropriately defined Laplacian, we obtain the existence of nontrivial solutions of sub-linear elliptic equations  $-Δu=λu-α(x)|u|^{q-1}u-f(x,u)$,  with zero boundary Dirichlet conditions. The results are obtained by using Mountain Pass Lemma and Saddle Point Theorem.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v24.n2.1

Journal of Partial Differential Equations, Vol. 24 (2011), Iss. 2 : pp. 97–113

Published online:    2011-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Self-similar fractal

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