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Positive Solutions of a Nonlinear Fourth-Order Dynamic Eigenvalue Problem on Time Scales
Joint Authors
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-05-28
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
Let T be a time scale and a,b∈T, a<ρ2(b).
We study the nonlinear fourth-order eigenvalue problem on T, uΔ4(t)=λh(t)f(u(t),uΔ2(t)), t∈[a,ρ2(b)]T, u(a)=uΔ(σ(b))=uΔ2(a)=uΔ3(ρ(b))=0 and obtain the existence and nonexistence of positive solutions when 0<λ≤λ* and λ>λ*, respectively, for some λ*.
The main tools to prove the existence results are the Schauder fixed point theorem and the upper and lower solution method.
American Psychological Association (APA)
Luo, Hua& Gao, Chenghua. 2012. Positive Solutions of a Nonlinear Fourth-Order Dynamic Eigenvalue Problem on Time Scales. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-17.
https://search.emarefa.net/detail/BIM-499069
Modern Language Association (MLA)
Luo, Hua& Gao, Chenghua. Positive Solutions of a Nonlinear Fourth-Order Dynamic Eigenvalue Problem on Time Scales. Abstract and Applied Analysis No. 2012 (2012), pp.1-17.
https://search.emarefa.net/detail/BIM-499069
American Medical Association (AMA)
Luo, Hua& Gao, Chenghua. Positive Solutions of a Nonlinear Fourth-Order Dynamic Eigenvalue Problem on Time Scales. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-17.
https://search.emarefa.net/detail/BIM-499069
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-499069