A class of semilinear elliptic equations on the Sierpinski gasket. Issue 15 (18th November 2021)

• Record Type: Journal Article
• Authors: Kar, Rasmita; Badajena, A. K.
• Is Part Of: Applicable analysis. Volume 100:Issue 15(2021)
• Page Start: 3212
• Page End: 3219
• Publication Date: 2021-11-18
• Subjects: Sierpinski gasket -- semilinear elliptic equations -- fractal domains -- monotone operators; 35J60 -- 28A80 -- 47H05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1713313
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We study the existence of a weak (strong) solution for the semilinear elliptic problem 1 − Δ u ( x ) − λ g ( x ) u ( x ) = − f ( x, u ( x ) ) i n V ∖ V 0 u = 0 o n V 0, where V is the Sierpiński gasket in R N − 1 ( N ≥ 2 ), V 0 is its boundary (consisting of its N corners) and λ is a real parameter. Here g : V → R and f : V × R → R are functions satisfying suitable hypotheses.