Existence of solutions for Dirichlet elliptic problems with discontinuous nonlinearity. (August 2020)

• Record Type: Journal Article
• Authors: Yuan, Ziqing; Yu, Jianshe
• Is Part Of: Nonlinear analysis. Volume 197(2020)
• Publication Date: 2020-08
• Subjects: 35J85 -- 47J30 -- 49J52; Dual method -- Variational method -- Definite sign solutions -- Sign-changing solution -- Discontinuous problems; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111848
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we concern with definite sign and sign-changing solutions of a class of discontinuous problems. By using the dual method, we overcome the difficulty of non-differentiability and obtain the existence results of definite sign solution and a sign-changing solutions on the Nehari manifold for the discontinuous problems. Some continuous results are extended to the discontinuous cases.