Infinitely many solutions for a class of nonlinear elliptic problems on fractals
Gabriele Bonanno, Giovanni Molica Bisci, Vicenţiu D. Rădulescu · Comptes Rendus Mathématique · 2012
We study the nonlinear problem Δ u + a ( x ) u = λ g ( x ) f ( u ) in V ∖ V 0 , u = 0 on V 0 , where V is the Sierpiński gasket, V 0 is its intrinsic boundary, Δ denotes the weak Laplace operator, λ is a positive parameter, and f has an oscillatory behaviour either near the origin or at infinity. In both cases, we establish the existence of infinitely many solutions, which either converge to zero or have larger and larger energies.