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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Positive solutions of a logistic equation on unbounded intervals
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by Li Ma and Xingwang Xu PDF
Proc. Amer. Math. Soc. 130 (2002), 2947-2958 Request permission


In this paper, we study the existence of positive solutions of a one-parameter family of logistic equations on $R_+$ or on $R$. 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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Additional Information
  • Li Ma
  • Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
  • MR Author ID: 293769
  • Email:
  • Xingwang Xu
  • Affiliation: Department of Mathematics, The National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
  • Email:
  • Received by editor(s): October 9, 2000
  • Received by editor(s) in revised form: May 3, 2001
  • Published electronically: April 22, 2002
  • Additional Notes: The work of the first author was partially supported by the 973 project of China, a grant from the Ministry of Education, and a scientific grant of Tsinghua University at Beijing. The authors thank the referee for helpful corrections.
  • Communicated by: Carmen C. Chicone
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 2947-2958
  • MSC (1991): Primary 34B09, 35J65
  • DOI:
  • MathSciNet review: 1908918