Qualitative analysis of gradient-type systems with oscillatory nonlinearities on the Sierpiński gasket

Abstract

Under an appropriate oscillating behavior either at zero or at infinity of the nonlinear data, the existence of a sequence of weak solutions for parametric quasilinear systems of the gradient-type on the Sierpiński gasket is proved. Moreover, by adopting the same hypotheses on the potential and in presence of suitable small perturbations, the same conclusion is achieved. The approach is based on variational methods and on certain analytic and geometrical properties of the Sierpiński fractal as, for instance, a compact embedding result due to Fukushima and Shima.

Keywords

Sierpiński gasket / Nonlinear elliptic equation / Dirichlet form / Weak Laplacian

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