Neumann problem driven by discontinuous nonlinearity

This is the authors' abstract. We don't add key points for this paper.

This paper is devoted to the study of a class of elliptic p-Laplacian Neumann problems (pLNP) involving a discontinuous power nonlinearity on a metric measure space. The main difficulties of this paper are twofold. On one hand, the framework of the studied problem is assumed in a metric measure space, rather than a Euclidean space. On the other hand, the presence of discontinuous nonlinearity leads to the invalidity of classical smooth variational methods. Under mild assumptions, we apply techniques from the theory of metric measure space and critical point theory of nonsmooth optimization to establish the nonemptyiness, convexity, and closedness of the solution set to the pLNP under consideration.