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The Existence of Positive Solutions for a Fourth-Order Difference Equation with Sum Form Boundary Conditions
Joint Authors
Lv, Xuefei
Liang, Yongchun
Ji, Yude
Guo, Yanping
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-16
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We consider the fourth-order difference equation: Δ(z(k+1)Δ3u(k-1))=w(k)f(k,u(k)), k∈{1,2,…,n-1} subject to the boundary conditions: u(0)=u(n+2)=∑i=1n+1g(i)u(i), aΔ2u(0)-bz(2)Δ3u(0)=∑i=3n+1h(i)Δ2u(i-2), aΔ2u(n)-bz(n+1)Δ3u(n-1)=∑i=3n+1h(i)Δ2u(i-2), where a,b>0 and Δu(k)=u(k+1)-u(k) for k∈{0,1,…,n-1}, f:{0,1,…,n}×[0,+∞)→[0,+∞) is continuous.
h(i) is nonnegative i∈{2,3,…,n+2}; g(i) is nonnegative for i∈{0,1,…,n}.
Using fixed point theorem of cone expansion and compression of norm type and Hölder’s inequality, various existence, multiplicity, and nonexistence results of positive solutions for above problem are derived, which extends and improves some known recent results.
American Psychological Association (APA)
Guo, Yanping& Lv, Xuefei& Ji, Yude& Liang, Yongchun. 2014. The Existence of Positive Solutions for a Fourth-Order Difference Equation with Sum Form Boundary Conditions. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1033848
Modern Language Association (MLA)
Guo, Yanping…[et al.]. The Existence of Positive Solutions for a Fourth-Order Difference Equation with Sum Form Boundary Conditions. Abstract and Applied Analysis No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-1033848
American Medical Association (AMA)
Guo, Yanping& Lv, Xuefei& Ji, Yude& Liang, Yongchun. The Existence of Positive Solutions for a Fourth-Order Difference Equation with Sum Form Boundary Conditions. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1033848
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033848