We study the steady state distribution of reaction diffusion equations with strong Allee effect type growth and constant yield harvesting (semipositone) in heterogeneous bounded habitats. Assuming the exterior of the habitat is completely hostile, we establish existence results for positive solutions. We also establish a multiplicity result for the non-harvested case. We obtain our results via the method of sub-super solutions.
A particular numerical method is discussed for solving the Hill–Wheeler equation, which is an integral equation that arises in the generator coordinate method analysis of problems in nuclear physics. The method is applicable to scattering problems with finite range potentials and exploits prior knowledge of the asymptotic form of the solution to convert the Hill–Wheeler equation into a Fredholm integral equation of the first kind. The resulting Fredholm equation is ill-posed, which often results in numerically unstable solutions. The method of regularization is used to produce numerically stable, approximate solutions. Optimizing the choice of regularization parameter is discussed and calculations are presented for an example problem.
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