Abstract
In this paper, the evolution of a dynamical system representing the population growth of Mozambique is analyzed. The correspondence between the boundary value problem and the integral equation is leveraged to address the issue of the local existence of solutions to the boundary value problem. The conclusion that the function converges to a function that is the unique solution to the boundary value problem is arrived at by way of constructing a sequence of approximations using Picard’s method of successive approximations and contraction mapping. The exponential function is globally Lipschitz, hence uniformly continuous; however, its solution does not converge to a fixed point implying that the population will grow without bounds as t→∞. The logistic model solves T (ϕ) = ϕ, whence T has a unique fixed point ϕ that is a continuous solution to the integral equation and consequently to the boundary value problem. Therefore, population growth is bounded. In addition, this function is locally Lipschitz and, therefore, not uniformly continuous.
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