Abstract
We study the nonlinear problem Δu+a(x)u=λg(x)f(u) in V∖V0, u=0 on V0, where V is the Sierpiński gasket, V0 is its intrinsic boundary, Δ denotes the weak Laplace operator, λ is a positive parameter, and f has an oscillatory behaviour either near the origin or at infinity. In both cases, we establish the existence of infinitely many solutions, which either converge to zero or have larger and larger energies.
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