On the Uniqueness of Nonnegative Solutions of Differential Inequalities with Gradient Terms on Riemannian Manifolds
نویسنده
چکیده
We investigate the uniqueness of nonnegative solutions to the following differential inequality div(A(x)|∇u|∇u) + V (x)u1 |∇u|2 ≤ 0, (1) on a noncompact complete Riemannian manifold, where A, V are positive measurable functions, m > 1, and σ1, σ2 ≥ 0 are parameters such that σ1 + σ2 > m− 1. Our purpose is to establish the uniqueness of nonnegative solution to (1) via very natural geometric assumption on volume growth.
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تاریخ انتشار 2014