Existence of a solution for a discontinuous problem involving the p-Laplacian operator - Tallana Chimarro, Darwin Xavier (2020)
I this work, we study a quasilinear boundary value problem involving the p-Laplacian operator on a bounded domain with smooth boundary. Into this boundary value problem, we consider a real-valued function f discontinuous at a point a, a bounded function h, and a function q belonging to a suitable Lebesgue space. Under certain conditions of growing on the function f and on the image of q, we give characterizations of the strong solutions of this problem. We also give sufficient conditions in order that points of local extremum become strongs solutions. A particular case of this boundary problem is considered as an application.