Existence of solutions for Dirichlet elliptic problems with discontinuous nonlinearity. (August 2020) - Yuan, Ziqing; Yu, Jianshe
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.