Oscillation criteria for second-order nonlinear neutral difference equations of mixed type

Some oscillation criteria are established for the second order nonlinear neutral difference equations of mixed type. Δ 2 ( x n + a x n - τ 1 ± b x n + τ 2 ) α = q n x n - σ 1 β + p n x x + σ 2 β , n ≥ n 0 where α and β are ratio of odd positive integers with β ≥ 1. Results obtained here generalize s...

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Published inAdvances in difference equations Vol. 2012; no. 1; pp. 1 - 10
Main Authors Thandapani, Ethiraju, Kavitha, Nagabhushanam, Pinelas, Sandra
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.01.2012
Springer Nature B.V
BioMed Central Ltd
Subjects
Analysis
Classification
Criteria
Difference and Functional Equations
Difference equations
Functional Analysis
Integers
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Ordinary Differential Equations
Oscillations
Partial Differential Equations
mixed type
oscillation
comparison theorems
Neutral difference equation
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Summary:Some oscillation criteria are established for the second order nonlinear neutral difference equations of mixed type. Δ 2 ( x n + a x n - τ 1 ± b x n + τ 2 ) α = q n x n - σ 1 β + p n x x + σ 2 β , n ≥ n 0 where α and β are ratio of odd positive integers with β ≥ 1. Results obtained here generalize some of the results given in the literature. Examples are provided to illustrate the main results. 2010 Mathematics Subject classification: 39A10 .
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ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/1687-1847-2012-4