A class of semilinear elliptic equations on the Sierpinski gasket. Issue 15 (18th November 2021) - Kar, Rasmita; Badajena, A. K.
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.