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

Brigitte E. Breckner, Dušan Repovš, Csaba Varga

Published 2016-02-19Version 1

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.