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 in | Advances in difference equations Vol. 2012; no. 1; pp. 1 - 10 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.01.2012
Springer Nature B.V BioMed Central Ltd |
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| Abstract | 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
. |
|---|---|
| AbstractList | Some oscillation criteria are established for the second order nonlinear neutral difference equations of mixed type. [Equation not available: see fulltext.] where alpha and beta are ratio of odd positive integers with beta greater than or equal to 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. 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 . Some oscillation criteria are established for the second order nonlinear neutral difference equations of mixed type. [Equation not available: see fulltext.] where [alpha] and [beta] are ratio of odd positive integers with [beta] â[per thousand]¥ 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.[PUBLICATION ABSTRACT] Some oscillation criteria are established for the second order nonlinear neutral difference equations of mixed type.Δ2(xn+axn-τ1±bxn+τ2)α=qnxn-σ1β+pnxx+σ2β,n≥n0where 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. |
| ArticleNumber | 4 |
| Author | Kavitha, Nagabhushanam Pinelas, Sandra Thandapani, Ethiraju |
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| Cites_doi | 10.1007/978-94-015-9401-1 10.1006/jmaa.1998.6001 10.1093/oso/9780198535829.001.0001 10.1080/10236190903032708 10.1016/S0895-7177(99)00115-6 10.1155/9789775945198 10.1016/S0096-3003(02)00631-8 10.1201/9781420027020 |
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| Copyright | Thandapani et al; licensee Springer. 2012. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Springer International Publishing AG 2012 |
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| References | AgarwalRPGraceSRThe oscillation of certain difference equationsMath Comput Model1999307783170239210.1016/S0895-7177(99)00115-6 JiangJOscillation of second order nonlinear neutral delay difference equationsAppl Math Comput2003146791801200858810.1016/S0096-3003(02)00631-8 AgarwalRPGraceSROscillation theorems for certain difference equations2000299308Dyna. Syst. Appl AgarwalRPBohnerMGraceSRO'ReganDDiscrete Oscillation Theory2005New YorkHindawi Publ. Corporation10.1155/9789775945198 HardyGHLittlewoodJEPolyaGInequalities19982CambridgeCambridge Univ Press GraceSROscillation of certain difference equations of mixed typeJ Math Anal Appl1998224241254163745310.1006/jmaa.1998.6001 AgarwalRPDifference Equations and Inequalities20002New YorkMarcel Dekkar MigdaMMigdaJOscillatory and asymptotic properties of solutions of even order neutral difference equationsJ Diff Equ Appl20091510771084256913610.1080/10236190903032708 GyoriILaddasGOscillation Theory of Delay Differential Equations1991OxfordClarendon Press M Migda (124_CR4) 2009; 15 J Jiang (124_CR8) 2003; 146 RP Agarwal (124_CR2) 2005 RP Agarwal (124_CR5) 1999; 30 GH Hardy (124_CR9) 1998 RP Agarwal (124_CR3) 2000 RP Agarwal (124_CR1) 2000 SR Grace (124_CR6) 1998; 224 I Gyori (124_CR7) 1991 |
| References_xml | – reference: HardyGHLittlewoodJEPolyaGInequalities19982CambridgeCambridge Univ Press – reference: AgarwalRPGraceSROscillation theorems for certain difference equations2000299308Dyna. Syst. Appl – reference: GyoriILaddasGOscillation Theory of Delay Differential Equations1991OxfordClarendon Press – reference: AgarwalRPGraceSRThe oscillation of certain difference equationsMath Comput Model1999307783170239210.1016/S0895-7177(99)00115-6 – reference: GraceSROscillation of certain difference equations of mixed typeJ Math Anal Appl1998224241254163745310.1006/jmaa.1998.6001 – reference: MigdaMMigdaJOscillatory and asymptotic properties of solutions of even order neutral difference equationsJ Diff Equ Appl20091510771084256913610.1080/10236190903032708 – reference: AgarwalRPDifference Equations and Inequalities20002New YorkMarcel Dekkar – reference: AgarwalRPBohnerMGraceSRO'ReganDDiscrete Oscillation Theory2005New YorkHindawi Publ. Corporation10.1155/9789775945198 – reference: JiangJOscillation of second order nonlinear neutral delay difference equationsAppl Math Comput2003146791801200858810.1016/S0096-3003(02)00631-8 – start-page: 299 volume-title: Oscillation theorems for certain difference equations year: 2000 ident: 124_CR3 doi: 10.1007/978-94-015-9401-1 – volume: 224 start-page: 241 year: 1998 ident: 124_CR6 publication-title: J Math Anal Appl doi: 10.1006/jmaa.1998.6001 – volume-title: Oscillation Theory of Delay Differential Equations year: 1991 ident: 124_CR7 doi: 10.1093/oso/9780198535829.001.0001 – volume-title: Inequalities year: 1998 ident: 124_CR9 – volume: 15 start-page: 1077 year: 2009 ident: 124_CR4 publication-title: J Diff Equ Appl doi: 10.1080/10236190903032708 – volume: 30 start-page: 77 year: 1999 ident: 124_CR5 publication-title: Math Comput Model doi: 10.1016/S0895-7177(99)00115-6 – volume-title: Discrete Oscillation Theory year: 2005 ident: 124_CR2 doi: 10.1155/9789775945198 – volume: 146 start-page: 791 year: 2003 ident: 124_CR8 publication-title: Appl Math Comput doi: 10.1016/S0096-3003(02)00631-8 – volume-title: Difference Equations and Inequalities year: 2000 ident: 124_CR1 doi: 10.1201/9781420027020 |
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| Snippet | 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... Some oscillation criteria are established for the second order nonlinear neutral difference equations of mixed type. [Equation not available: see fulltext.]... Some oscillation criteria are established for the second order nonlinear neutral difference equations of mixed... |
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| SubjectTerms | 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 |
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| Title | Oscillation criteria for second-order nonlinear neutral difference equations of mixed type |
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