On S-shaped Bifurcation Curves for Multi-parameter Positone Problems

V. Anuradha; R. Shivaji; Jianping Zhu

doi:10.1016/0096-3003(94)90174-0

On S-shaped Bifurcation Curves for Multi-parameter Positone Problems

V. Anuradha
, R. Shivaji
, Jianping Zhu

Mississippi State University

Research output: Contribution to journal › Article › peer-review

Abstract

<h2 id="x-x-x-x-section_abstract"> Abstract </h2> We study the existence of multiple positive solutions to the two point boundary value problem -u″(x) = &lthree;f(u(x)); O< x < 1 u(0) = 0 = u(1) + αu′(1), where &lthree; > 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.

Original language	American English
Journal	Applied Mathematics and Computation
Volume	65
DOIs	https://doi.org/10.1016/0096-3003(94)90174-0
State	Published - Sep 1 1994

Disciplines

Applied Mathematics

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title = "On S-shaped Bifurcation Curves for Multi-parameter Positone Problems",

abstract = " Abstract We study the existence of multiple positive solutions to the two point boundary value problem -u\″(x) = \&lthree;f(u(x)); O< x < 1 u(0) = 0 = u(1) + \αu\′(1), where \&lthree; > 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. ",

author = "V. Anuradha and R. Shivaji and Jianping Zhu",

note = "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.",

year = "1994",

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doi = "10.1016/0096-3003(94)90174-0",

language = "American English",

volume = "65",

journal = "Applied Mathematics and Computation",

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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) = &lthree;f(u(x)); O< x < 1 u(0) = 0 = u(1) + αu′(1), where &lthree; > 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) = &lthree;f(u(x)); O< x < 1 u(0) = 0 = u(1) + αu′(1), where &lthree; > 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 -

On S-shaped Bifurcation Curves for Multi-parameter Positone Problems

Abstract

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