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Positive solutions of a logistic equation on unbounded intervals

Authors: Li Ma and Xingwang Xu
Journal: Proc. Amer. Math. Soc. 130 (2002), 2947-2958
MSC (1991): Primary 34B09, 35J65
Published electronically: April 22, 2002
MathSciNet review: 1908918
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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
MR Author ID: 293769

Xingwang Xu
Affiliation: Department of Mathematics, The National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260

Keywords: Direct method, blow-up, positive solution
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
Article copyright: © Copyright 2002 American Mathematical Society