On the perturbed Gelfand equation from combustion theory
Abstract
For the perturbed Gelfand's equation on the unit ball in two dimensions, Y. Du and Y. Lou [4] proved that the curve of positive solutions is exactly S-shaped, for sufficiently small values of the secondary parameter. We present a simplified proof and some extensions. This problem is prominent in combustion theory, see e.g., the book of J. Bebernes and D. Eberly [1].
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