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2012 Positive Solutions of a Second-Order Nonlinear Neutral Delay Difference Equation
Zeqing Liu, Wei Sun, Jeong Sheok Ume, Shin Min Kang
Abstr. Appl. Anal. 2012: 1-30 (2012). DOI: 10.1155/2012/172939


The purpose of this paper is to study solvability of the second-order nonlinear neutral delay difference equation Δ ( a ( n , y a 1 n , , y a r n ) Δ ( y n + b n y n - τ ) ) + f ( n , y f 1 n , , y f k n ) = c n , n n 0 . By making use of the Rothe fixed point theorem, Leray-Schauder nonlinear alternative theorem, Krasnoselskill fixed point theorem, and some new techniques, we obtain some sufficient conditions which ensure the existence of uncountably many bounded positive solutions for the above equation. Five nontrivial examples are given to illustrate that the results presented in this paper are more effective than the existing ones in the literature.


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Zeqing Liu. Wei Sun. Jeong Sheok Ume. Shin Min Kang. "Positive Solutions of a Second-Order Nonlinear Neutral Delay Difference Equation." Abstr. Appl. Anal. 2012 1 - 30, 2012.


Published: 2012
First available in Project Euclid: 28 March 2013

zbMATH: 1259.39004
MathSciNet: MR3004909
Digital Object Identifier: 10.1155/2012/172939

Rights: Copyright © 2012 Hindawi


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