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Positive Solutions and Mann Iterations of a Fourth Order Nonlinear Neutral Delay Differential Equation

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Listed:
  • Zeqing Liu
  • Jingjing Zhu
  • Jeong Sheok Ume
  • Shin Min Kang

Abstract

This paper deals with a fourth order nonlinear neutral delay differential equation. By using the Banach fixed point theorem, we establish the existence of uncountably many bounded positive solutions for the equation, construct several Mann iterative sequences with mixed errors for approximating these positive solutions, and discuss some error estimates between the approximate solutions and these positive solutions. Seven nontrivial examples are given.

Suggested Citation

  • Zeqing Liu & Jingjing Zhu & Jeong Sheok Ume & Shin Min Kang, 2014. "Positive Solutions and Mann Iterations of a Fourth Order Nonlinear Neutral Delay Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:105719
    DOI: 10.1155/2014/105719
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    References listed on IDEAS

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    1. Zeqing Liu & Lin Chen & Shin Min Kang & Sun Young Cho, 2011. "Existence of Nonoscillatory Solutions for a Third‐Order Nonlinear Neutral Delay Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
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