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

David Ruiz; Antonio Suárez

doi:10.1017/S0308210505000491

Abstract

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The main goal of this work is to study the existence and uniqueness of a 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.

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

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