Nonlinear elliptical equations on the Sierpiński gasket
The authors investigate a question on the nontrivial solutions for the equation \(\Delta u + a(x)u=f(x,u)\) with zero Dirichlet conditions on the Sierpiński gasket. There are results both for a standard (in this theory) Laplacian and for a weak one. Some of the used general functional tools are: mountain pass theorem and saddle point theorem.
scientific article; zbMATH DE number 1417581