Mathematical Sciences: Semi-Positone Problems II

本课题将研究一类半正椭圆型 算子及其相关的边值问题。 的 有趣的情况下，非线性是负的， 起源，将被调查和存在性和分歧 将分析正解。结果将进一步 我们对这些解的性质的理解， 作为解集的全局性质。 半正椭圆方程发生在一个 各种各样的真实的生活现象，例如预测 一个种群的增长或减少， 竞争或收获。 主要结果将是适用的 从感染介质中的细菌密度 对公司生存能力的期望 激烈的竞争。

This project will study a class of semipositive elliptic operators and their associated boundary value problems. The interesting case, where the nonlinearity is negative at the origin, will be investigated and the existence and bifurcation of the positive solutions will be analyzed. The results will further our understanding of the properties of these solutions, as well as the global nature of the set of solutions. Semipositive elliptic equations occur in the modeling of a wide variety of real life phenomena such as predicting the rate of growth or depletion of a population subject to predators, competition, or harvesting. The main results will be applicable in areas ranging from density of bacteria in an infected medium to expectation of the survivability of a company subject to strong competition.