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This paper presents results on a class of Kirchhoff problems, using the theory established in a previous work Ricceri01. Specifically, we focus on the Sierpi\’nski gasket (V,\|·\|) in (^n-1,|·|), where n≥ 2, and V_0 is its intrinsic boundary consisting of n corners. We consider a continuous function f:→ and show that the following two statements are equivalent: (i) the restriction of f to [-(2n+3)2π 4, (2n+3)2π 4] is not constant, and (ii) for every convex set Θ that is dense in C^0(V)× C^0(V), there exists (α,β)Θ such that a class of Kirchhoff problems, as follows: equation* {arrayll -(\|u\|^2)Δ u+t^2u(t)=β(t)f(u(t))+α(t),tVV_0 u(t)=0,tV_0, \|u\|^2<π2 array. equation* has at least two classical solutions. , number=2, journal=Nonlinear Studies, year=2024, month=May