A critical anisotropic problem with discontinuous nonlinearities. (June 2019)

• Record Type: Journal Article
• Authors: Figueiredo, Giovany M.; Silva, Julio R.S.
• Is Part Of: Nonlinear analysis. Volume 47(2019)
• Page Start: 364
• Page End: 372
• Publication Date: 2019-06
• Subjects: Anisotropic problem -- Critical growth -- Discontinuous nonlinearity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.11.008
• Languages: English
• ISSNs: 1468-1218

Abstract

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.