Existence results for nonlinear elliptic problems on fractal domains

Abstract

Some existence results for a parametric Dirichlet problem defined on the Sierpiński fractal are proved. More precisely, a critical point result for differentiable functionals is exploited in order to prove the existence of a well-determined open interval of positive eigenvalues for which the problem admits at least one non-trivial weak solution.

Keywords

• sierpiński gasket
• nonlinear elliptic equation
• dirichlet form
• weak laplacian
• 35j20
• 28a80
• 35j25
• 35j60
• 47j30
• 49j52