Existence and uniqueness of positive solution of a logistic equation with nonlinear gradient term

Abstract

The main goal of this work is to study the existence and uniqueness of positive solution of a logistic equation including a nonlinear gradient term. In particular, we use local and global bifurcation together with some a-priori estimates. To prove uniqueness, the sweeping method of Serrin is employed.Ministerio de Ciencia y TecnologíaJunta de Andalucí