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On S-shaped Bifurcation Curves for Multi-parameter Positone Problems
Applied Mathematics and Computation
  • V. Anuradha, Mississippi State University
  • R. Shivaji, Mississippi State University
  • Jianping Zhu, Cleveland State University
Document Type
Article
Publication Date
9-1-1994
Disciplines
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.
Comments

This research was supported in part by NSF Grant DMS-9215027.

DOI
10.1016/0096-3003(94)90174-0
Citation Information
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.