On Uniqueness of Solutions to the Boundary Value Problems on the Sierpiński Gasket. (1st July 2021)

• Record Type: Journal Article
• Authors: Stegliński, Robert
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 7(2021)
• Page Start: 809
• Page End: 818
• Publication Date: 2021-07-01
• Subjects: Dependence on parameters -- Sierpiński gasket -- unique solution; 28A80 -- 35J91; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1931310
• Languages: English
• ISSNs: 0163-0563

Abstract

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.