S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation
Joint Authors
Ma, Ruyun
Wang, Jinxiang
Wen, Jin
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-07-24
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
We investigate the existence of S-shaped connected component in the set of positive solutions of the fourth-order boundary value problem: u′′′′x=λhxfux, x∈(0,1),u(0)=u(1)=u′′0=u′′1=0, where λ>0 is a parameter, h∈C[0,1], and f∈C[0,∞) with f0≔lims→0(f(s)/s)=∞.
We develop a bifurcation approach to deal with this extreme situation by constructing a sequence of functions f[n] satisfying f[n]→f and (f[n])0→∞.
By studying the auxiliary problems, we get a sequence of unbounded connected components C[n], and, then, we find an unbounded connected component C in the set of positive solutions of the fourth-order boundary value problem which satisfies 0,0∈C⊂limsupC[n] and is S-shaped.
American Psychological Association (APA)
Wang, Jinxiang& Ma, Ruyun& Wen, Jin. 2017. S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation. Journal of Function Spaces،Vol. 2017, no. 2017, pp.1-8.
https://search.emarefa.net/detail/BIM-1176295
Modern Language Association (MLA)
Wang, Jinxiang…[et al.]. S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation. Journal of Function Spaces No. 2017 (2017), pp.1-8.
https://search.emarefa.net/detail/BIM-1176295
American Medical Association (AMA)
Wang, Jinxiang& Ma, Ruyun& Wen, Jin. S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation. Journal of Function Spaces. 2017. Vol. 2017, no. 2017, pp.1-8.
https://search.emarefa.net/detail/BIM-1176295
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1176295