Abstract
In this paper, we study the existence of positive solutions of a one-parameter family of logistic equations on R + R_+ or on R R . These equations are stationary versions of the Fisher equations and the KPP equations. We also study the blow-up region of a sequence of the solutions when the parameter approaches a critical value and the non-existence of positive solutions beyond the critical value. We use the direct method and the sub and super solution method.
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