Abstract
In this paper, a reaction–diffusion system known as a bimolecular model with autocatalysis and saturation law is considered. Firstly, we briefly obtain some characterizations for the positive solutions, including the a priori estimate of the positive solutions and the nonexistence of non-constant positive solution. Secondly, we emphatically discusses the bifurcation from the unique positive constant solution with both simple eigenvalues and double eigenvalues in one-dimensional case. Meanwhile, some other existence results are shown to supplement the analytical conclusions with the degree theory in N dimensional case.
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The authors would like to express their sincere thanks to the anonymous referees for their valuable suggestions.
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The work is supported by the Natural Science Foundation of China (Nos. 11771262, 11671243) and the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2018JQ1021).
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Yang, W., Wei, Z., Jiang, H. et al. The existence of steady states for a bimolecular model with autocatalysis and saturation law. Z. Angew. Math. Phys. 69, 131 (2018). https://doi.org/10.1007/s00033-018-1024-8
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DOI: https://doi.org/10.1007/s00033-018-1024-8