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Positive solutions of a logistic equation on unbounded intervals

Author(s): Li Ma; Xingwang Xu
Journal: Proc. Amer. Math. Soc. 130 (2002), 2947-2958.
MSC (1991): Primary 34B09, 35J65
Posted: April 22, 2002
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Abstract: 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
Email: lma@math.tsinghua.edu.cn

Xingwang Xu
Affiliation: Department of Mathematics, The National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
Email: matxuxw@math.nus.edu.sg

DOI: 10.1090/S0002-9939-02-06405-5
PII: S 0002-9939(02)06405-5
Keywords: Direct method, blow-up, positive solution
Received by editor(s): October 9, 2000
Received by editor(s) in revised form: May 3, 2001
Posted: 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 of article: Copyright 2002, American Mathematical Society

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