## 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

## 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.## References

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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: 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
- 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: https://doi.org/10.1090/S0002-9939-02-06405-5
- MathSciNet review: 1908918