Mathematical Sciences: Semi-Positone Problems II

本课题研究一类半正椭圆算子及其边值问题。研究了非线性在原点为负的有趣情况，并分析了正解的存在性和分岔性。这些结果将进一步加深我们对这些解的性质以及解集的全局性质的理解。半正椭圆方程出现在各种各样的现实生活现象的建模中，例如预测受捕食者、竞争或收获影响的种群的增长率或耗竭率。主要结果将适用于从受感染培养基中的细菌密度到公司在激烈竞争下的生存能力预期等领域。

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.