Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket

Gabriele Bonanno; Giovanni Molica Bisci; Vicenţiu Rădulescu

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 4, page 941-953
  • ISSN: 1292-8119

Abstract

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Under an appropriate oscillating behaviour either at zero or at infinity of the nonlinear term, the existence of a sequence of weak solutions for an eigenvalue Dirichlet problem on the Sierpiński gasket is proved. Our approach is based on variational methods and on some analytic and geometrical properties of the Sierpiński fractal. The abstract results are illustrated by explicit examples.

How to cite

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Bonanno, Gabriele, Bisci, Giovanni Molica, and Rădulescu, Vicenţiu. "Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket." ESAIM: Control, Optimisation and Calculus of Variations 18.4 (2012): 941-953. <http://eudml.org/doc/272940>.

@article{Bonanno2012,
abstract = {Under an appropriate oscillating behaviour either at zero or at infinity of the nonlinear term, the existence of a sequence of weak solutions for an eigenvalue Dirichlet problem on the Sierpiński gasket is proved. Our approach is based on variational methods and on some analytic and geometrical properties of the Sierpiński fractal. The abstract results are illustrated by explicit examples.},
author = {Bonanno, Gabriele, Bisci, Giovanni Molica, Rădulescu, Vicenţiu},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Sierpiński gasket; nonlinear elliptic equation; Dirichlet form; weak laplacian; weak Laplacian},
language = {eng},
number = {4},
pages = {941-953},
publisher = {EDP-Sciences},
title = {Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket},
url = {http://eudml.org/doc/272940},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Bonanno, Gabriele
AU - Bisci, Giovanni Molica
AU - Rădulescu, Vicenţiu
TI - Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2012
PB - EDP-Sciences
VL - 18
IS - 4
SP - 941
EP - 953
AB - Under an appropriate oscillating behaviour either at zero or at infinity of the nonlinear term, the existence of a sequence of weak solutions for an eigenvalue Dirichlet problem on the Sierpiński gasket is proved. Our approach is based on variational methods and on some analytic and geometrical properties of the Sierpiński fractal. The abstract results are illustrated by explicit examples.
LA - eng
KW - Sierpiński gasket; nonlinear elliptic equation; Dirichlet form; weak laplacian; weak Laplacian
UR - http://eudml.org/doc/272940
ER -

References

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