Existence of solutions for a non-local equation on the Sierpiński gasket.

This research paper introduces novel findings regarding a specific class of Kirchhoff problems. Building upon the theoretical groundwork established in a previous work by Ricceri [15], the paper centers its investigation on the Sierpiński gasket (V, |•|) situated in (Rn-1,- |•|), where n≥ 2. The intrinsic boundary of the Sierpiński gasket, denoted as Vo, comprises n corners. Under certain conditions, we prove that a Kirchhoff problem has two classical solutions in the space H0¹(V). [ABSTRACT FROM AUTHOR]