Positive Solutions for a Higher-Order Nonlinear Neutral Delay Differential Equation
Joint Authors
Ume, Jeong Sheok
Kang, Shin Min
Jia, Ming
Liu, Zeqing
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-10-11
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
This paper deals with the higher-order nonlinear neutral delay differential equation (dn/dtn)[x(t)+∑i=1mpi(t)x(Ti(t))]+(dn−1/dtn−1)f(t,x(α1(t)),…,x(αk(t)))+h(t,x(β1(t)),…,x(βk(t)))=g(t), t≥to, where n,m,k∈ℕ, pi,τi,βj,g∈C([to,+∞),ℝ), αj∈Cn−1([to,+∞),ℝ), f∈Cn−1([to,+∞)×ℝk,ℝ), h∈C([to,+∞)×ℝk,ℝ), and limt→+∞τi(t)=limt→+∞αj(t)=limt→+∞βj(t)=+∞, i∈{1,2,…,m}, j∈{1,2,…,k}.
By making use of the Leray-Schauder nonlinear alterative theorem, we establish the existence of uncountably many bounded positive solutions for the above equation.
Our results improve and generalize some corresponding results in the field.
Three examples are given which illustrate the advantages of the results presented in this paper.
American Psychological Association (APA)
Liu, Zeqing& Jia, Ming& Ume, Jeong Sheok& Kang, Shin Min. 2011. Positive Solutions for a Higher-Order Nonlinear Neutral Delay Differential Equation. Abstract and Applied Analysis،Vol. 2011, no. 2011, pp.1-16.
https://search.emarefa.net/detail/BIM-463965
Modern Language Association (MLA)
Liu, Zeqing…[et al.]. Positive Solutions for a Higher-Order Nonlinear Neutral Delay Differential Equation. Abstract and Applied Analysis No. 2011 (2011), pp.1-16.
https://search.emarefa.net/detail/BIM-463965
American Medical Association (AMA)
Liu, Zeqing& Jia, Ming& Ume, Jeong Sheok& Kang, Shin Min. Positive Solutions for a Higher-Order Nonlinear Neutral Delay Differential Equation. Abstract and Applied Analysis. 2011. Vol. 2011, no. 2011, pp.1-16.
https://search.emarefa.net/detail/BIM-463965
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-463965