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Volume 24, Issue 2
Sublinear Elliptic Equation on Fractal Domains

Zhenya He

DOI: 10.4208/jpde.v24.n2.1

J. Part. Diff. Eq., 24 (2011), pp. 97-113.

Published online: 2011-05

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  • 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.

  • Keywords

Self-similar fractal saddle point theorem elliptic equation mountain pass lemma Laplacian operator

  • AMS Subject Headings

35K55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-24-97, author = {Zhenya He }, title = {Sublinear Elliptic Equation on Fractal Domains}, journal = {Journal of Partial Differential Equations}, year = {2011}, volume = {24}, number = {2}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v24.n2.1}, url = {http://global-sci.org/intro/article_detail/jpde/5200.html} }
TY - JOUR T1 - Sublinear Elliptic Equation on Fractal Domains AU - Zhenya He JO - Journal of Partial Differential Equations VL - 2 SP - 97 EP - 113 PY - 2011 DA - 2011/05 SN - 24 DO - http://doi.org/10.4208/jpde.v24.n2.1 UR - https://global-sci.org/intro/article_detail/jpde/5200.html KW - Self-similar fractal KW - saddle point theorem KW - elliptic equation KW - mountain pass lemma KW - Laplacian operator AB -

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.

Zhenya He . (2011). Sublinear Elliptic Equation on Fractal Domains. Journal of Partial Differential Equations. 24 (2). 97-113. doi:10.4208/jpde.v24.n2.1
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