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arXiv · 1602.06092

On the existence of three solutions for the Dirichlet problem on the Sierpinski gasket

Brigitte E. Breckner·Dušan Repovš·Csaba Varga
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Abstract

We apply a recently obtained three critical points theorem of B. Ricceri to prove the existence of at least three solutions of certain two-parameters Dirichlet problems defined on the Sierpinski gasket. We also show the existence of at least three nonzero solutions of certain perturbed two-parameters Dirichlet problems on the Sierpinski gasket, using both the mountain pass theorem of Ambrosetti-Rabinowitz and that of Pucci-Serrin.

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Brigitte E. Breckner, Dušan Repovš, Csaba Varga. 2016-02-19. On the existence of three solutions for the Dirichlet problem on the Sierpinski gasket. https://doi.org/10.1016/j.na.2010.06.064

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