On the existence of three solutions for the Dirichlet problem on the Sierpinski gasket |
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| Authors: | Brigitte E Breckner Dušan Repovš |
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| Institution: | a Babe?-Bolyai University, Faculty of Mathematics and Computer Science, Kog?lniceanu street 1, 400084 Cluj-Napoca, Romaniab Institute of Mathematics, Physics and Mechanics, P.O. Box 2964, SI-1001 Ljubljana, Slovenia |
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| Abstract: | We apply a recently obtained three-critical-point theorem of B. Ricceri to prove the existence of at least three solutions of certain two-parameter Dirichlet problems defined on the Sierpinski gasket. We also show the existence of at least three nonzero solutions of certain perturbed two-parameter Dirichlet problems on the Sierpinski gasket, using both the mountain pass theorem of Ambrosetti and Rabinowitz and that of Pucci and Serrin. |
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| Keywords: | primary 35J20 secondary 28A80 35J25 35J60 47J30 49J52 |
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