Geodesic
Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 941-953

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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.

DOI : 10.1051/cocv/2011199
Classification : 35J20, 28A80, 35J25, 35J60, 47J30, 49J52
Keywords: Sierpiński gasket, nonlinear elliptic equation, Dirichlet form, weak laplacian 
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     title = {Variational analysis for a nonlinear elliptic problem on the {Sierpi\'nski} gasket},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {941--953},
     publisher = {EDP-Sciences},
     volume = {18},
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     doi = {10.1051/cocv/2011199},
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     zbl = {1278.35088},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011199/}
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Bonanno, Gabriele; Molica Bisci, Giovanni; Rădulescu, Vicenţiu. Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 941-953. doi: 10.1051/cocv/2011199

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