A critical anisotropic problem with discontinuous nonlinearities. (June 2019) - Figueiredo, Giovany M.; Silva, Julio R.S.
Abstract: In this paper we prove existence of a nonnegative solution for nonlinear anisotropic elliptic equations of the type − [ ∑ i = 1 N ∂ ∂ x i ( | ∂ u ∂ x i | p i − 2 ∂ u ∂ x i ) ] = f ( x, u ) + | u | p ∗ − 2 u in Ω, u = 0 on ∂ Ω, where Ω is a smooth bounded domain in R N with homogeneous Dirichlet boundary conditions. Here f can have an uncountable set of discontinuity points.