Mathematical Sciences: Semi-Positone Problems II

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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.