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| Qualitative Analysis of Gradient-Type Systems with Oscillatory Nonlinearities on the Sierpi′nski Gasket |
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Citation： |
Gabriele BONANNO,Giovanni MOLICA BISCI,Vicent¸iu R˘ADULESCU.Qualitative Analysis of Gradient-Type Systems with Oscillatory Nonlinearities on the Sierpi′nski Gasket[J].Chinese Annals of Mathematics B,2013,34(3):381~398 |
| Page view： 3282
Net amount： 2288 |
Authors： |
Gabriele BONANNO; Giovanni MOLICA BISCI; Vicent?iu R?ADULESCU; |
Foundation： |
Grant CNCS PCE 47/2011 (Qualitative and Numerical Analysis of Nonlinear Problems on Fractals),the GNAMPA Project (Esistenza e molteplicit′a di soluzioni per problemi differenziali non lineari) 2012 |
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| 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 Sierpi′nski 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 Sierpi′nski fractal as, for instance, a compact embedding result due to Fukushima and Shima. |
Keywords： |
Sierpi′nski gasket, Nonlinear elliptic equation, Dirichlet form, Weak Laplacian |
Classification： |
35J20, 28A80, 35J25, 35J60, 47J30, 49J52 |
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