标题： 关于流形上的逻辑型方程的存在性和非存在性结果 显示英文标题

标题： Existence and non-existence results for a logistic-type equation on manifolds

摘要： 我们研究了完备黎曼流形上广义逻辑斯蒂型方程的定态解。我们给出了正解存在和不存在的充分条件，这些条件依赖于系数的相对大小及其与流形几何特性的相互作用，而流形的几何特性主要通过测地球的体积增长率条件来体现。 显示英文摘要

摘要： We study the steady state solutions of a generalized logistic type equation on a complete Riemannian manifold. We provide sufficient conditions for existence, respectively non-existence of positive solutions, which depend on the relative size of the coefficients and their mutual interaction with the geometry of the manifold, which is mostly taken into account by means of conditions on the volume growth of geodesic balls.