Abstract
This paper ascertains the structure of the set of positive solutions of a degenerate weighted logistic equation with a continuous kinetic under non-classical mixed boundary conditions. After establishing the uniqueness of the positive solution and the existence of two global components of positive solutions, it is shown that any component must be a continuous curve. Further, some general sufficient conditions are provided, in terms of the weight functions involved in the setting of the model, so that it possesses exactly two components of positive solutions. The problem of finding out the total number of components in the general case remains open.
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