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

DOI:
https://doi.org/10.1090/S0002-9939-02-06405-5

Published electronically:
April 22, 2002

MathSciNet review:
1908918

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we study the existence of positive solutions of a one-parameter family of logistic equations on or on . 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:
https://doi.org/10.1090/S0002-9939-02-06405-5

Keywords:
Direct method,
blow-up,
positive solution

Received by editor(s):
October 9, 2000

Received by editor(s) in revised form:
May 3, 2001

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