On S-shaped Bifurcation Curves for Multi-parameter Positone Problems
Document Type
Article
Publication Date
9-1994
Publication Title
Applied Mathematics and Computation
Abstract
Abstract
We study the existence of multiple positive solutions to the two point boundary value problem
-u″(x) = ⋋f(u(x)); O< x < 1 u(0) = 0 = u(1) + αu′(1),
where ⋋ > 0, α > 0. Here f is a smooth function such that f > 0 on [0, r) for some 0 < r ≤ ∞. In particular, we consider the case when f is initially convex and then concave. We discuss sufficient conditions for the existence of at least three positive solutions for a certain range (independent of α) of λ. We apply our results to the nonlinearity which arises in combustion theory and to the nonlinearity (fixed), , which arises in chemical reactor theory.
Repository Citation
Anuradha, V., Shivaji, R., and Zhu, J. (1994). On S-shaped Bifurcation Curves for Multi-parameter Positone Problems. Applied Mathematics and Computation, 65(1-3), 171-182, doi: 10.1016/0096-3003(94)90174-0.
Original Citation
Anuradha, V., Shivaji, R., and Zhu, J. (1994). On S-shaped Bifurcation Curves for Multi-parameter Positone Problems. Applied Mathematics and Computation, 65(1-3), 171-182, doi: 10.1016/0096-3003(94)90174-0.
DOI
10.1016/0096-3003(94)90174-0
Volume
65
Issue
1-3
Comments
This research was supported in part by NSF Grant DMS-9215027.