On Uniqueness of Solutions to the Boundary Value Problems on the Sierpiński Gasket. (1st July 2021) - Stegliński, Robert
Abstract: Using the monotonicity methods, we obtain conditions for the existence of the unique weak solution of Dirichlet problem { Δ u ( x ) + a ( x ) u ( x ) = f ( x, u ( x ) ) x ∈ V \ V 0 u | V 0 = 0, considered on the Sierpiński gasket. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are also given. We also consider a problem with parameters and we prove the theorem about continuous dependence on parameters.