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Critical point approaches to Gradient-Type systems on the Sierpi\''{n}ski Gasket
Shapour Heidarkhani,Fang-Fang Liao,Ghasem A. Afrouzi,Amjad Salari
Keywords:Gradient-Type systems; Sierpi\''{n}ski gasket; Three solutions; Nonlinear elliptic equation; Variational methods; Critical point theory
      We investigate the existence of multiple solutions for parametric quasi-linear systems of the gradient-type on the Sierpi\''{n}ski gasket. We give some new criteria to guarantee that the systems have at least three weak solutions by using a variational method and some critical points theorems due to Ricceri. We extend and improve some recent results. Finally, we give two examples to illustrate the main results.