TY - JOUR
T1 - On S-shaped Bifurcation Curves for Multi-parameter Positone Problems
AU - Anuradha, V.
AU - Shivaji, R.
AU - Zhu, Jianping
N1 - 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.
PY - 1994/9/1
Y1 - 1994/9/1
N2 - 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.
AB - 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.
UR - https://engagedscholarship.csuohio.edu/scimath_facpub/72
UR - http://journals.ohiolink.edu/ejc/article.cgi?issn=00963003&issue=v65i1-3&article=171_osbcfmpp
U2 - 10.1016/0096-3003(94)90174-0
DO - 10.1016/0096-3003(94)90174-0
M3 - Article
VL - 65
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -