We prove a characterization theorem on the existence of one non-zero strong solution for elliptic equations defined on the Sierpiński gasket. More generally, the validity of our result can be checked ...studying elliptic equations defined on self-similar fractal domains whose spectral dimension ▫$\nu \in (0,2)$▫. Our theorem can be viewed as an elliptic version on fractal domains of a recent contribution obtained in a recent work of Ricceri for a two-point boundary value problem.
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