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Published in:
Calculus on Time Scales Read chapter Read first chapter

2019 | OriginalPaper | Chapter

6. Oscillations of First-Order Functional Dynamic Equations

Author : Svetlin G. Georgiev

Published in: Functional Dynamic Equations on Time Scales

Publisher: Springer International Publishing

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Abstract

Let \(\mathbb {T}\) be a time scale that is unbounded above with forward jump operator and delta differentiation operator σ and Δ, respectively.

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previous chapter Stability for First-Order Functional Dynamic Equations
next chapter Oscillations of Second-Order Linear Functional Dynamic Equations with a Single Delay
Literature
1.
M. Adivar and Y. Raffoul. Existence of Periodic Solutions in Totally Nonlinear Delay Dynamic Equations, Electron. J. Qual. Theory Differ. Equ., Spec. Ed. 1 (2009), 1–20.
2.
M. Adivar and Y. Raffoul. Shift Operators and Stability in Delayed Dynamic Equations, Rend. Sem. Mat. Univ. Politec. Torino, Vol. 68, 4,(2010), pp. 369–396.
3.
M. Adivar and Y. N. Raffoul. Existence of Periodic Solutions in Totally Nonlinear Delay Dynamic Equations, Electron. J. Qual. Theory Differ. Equ. 2009 (2009), 1–20.MathSciNetCrossRef
4.
R. Agarwal and M. Bohner. Quadratic Functionals for Second Order Matrix Equations on Time Scales, Nonlinear Analysis, 33(1998), pp. 675–692.MathSciNetCrossRef
5.
R. Agarwal, M. Bohner and S. Saker. Oscillation of Second Order Delay Dynamic Equations, Canadian Applied Mathematics Quarterly, Vol. 13, N. 1, 2005.
6.
R. Agarwal, M. Bohner. Basic Calculus on Time Scales and Some of its Applications, Results Math. 35 (1–2) (1999) 3–22.MathSciNetCrossRef
7.
R. Agarwal, M. Bohner, T. Li and C. Zhang. Oscillation Theorems for Fourth-Order Half-Linear Delay Dynamic Equations with Damping. Mediterr. J. Math. 11, 463–475 (2014).MathSciNetCrossRef
8.
R. Agarwal, M. Bohner, D. O’Regan and A. Peterson. Dynamic Equations on Time Scales: A Survey, J. Comput. Appl. Math. 141 (2002) 1–26.MathSciNetCrossRef
9.
R. Agarwal, D. O’Regan, and S.H. Saker. Oscillation Criteria for Second-Order Nonlinear Neutral Delay Dynamic Equations, Journal of Mathematical Analysis and Applications 300 (2004), no. 1, 203–217.MathSciNetCrossRef
10.
R. Agarwal, S. Grace and D. O’Regan. The Oscillation of Certain Higher-Order Functional Differential Equations. Math. Comput. Model. 37, 705–728 (2003).MathSciNetCrossRef
11.
R. Agarwal, M. Bohner, S. Tang, T. Li and C. Zhang. Oscillation and Asymptotic Behavior of Third-Order Nonlinear Retarded Dynamic Equations. Appl. Math. Comput. 219, 3600–3609 (2012).MathSciNetMATH
12.
R. Agarwal, M. Bohner, M, T. Li and C. Zhang. A Philos-Type Theorem for Third-Order Nonlinear Retarded Dynamic equations. Appl. Math. Comput. 249, 527–531 (2014).MathSciNetCrossRef
13.
R. Agarwal, M. Bohner, T. Li and C. Zhang. Hille and Nehari Type Criteria for Third-Order Delay Dynamic Equations. J. Differ. Equ. Appl. 19, 1563–1579 (2013).MathSciNetCrossRef
14.
A. Agwo. On the Oscillation of First Order Delay Dynamic Equations with Variable Coefficients, Rocky Mountain Journal of Mathematics, Vol. 38, N. 1, 2008.MathSciNetCrossRef
15.
B. Ahmad and S. Sivasundaram. Dynamics and Stability of Impulsive Hybrid Setvalued Integro-Differential Equations, Nonlinear Anal. 65 (2006) 2082–2093.MathSciNetCrossRef
16.
M. U. Akhmet. On the General Problem of Stability for Impulsive Differential Equations, J. Math. Anal. Appl. 288 (2003) 182–196.MathSciNetCrossRef
17.
M. U. Akhmet, J. Alzabut and A. Zafer. Perron’s Theorem for Linear Impulsive Differential Equations with Distributed Delay, J. Comput. Appl. Math. 193(2006)204–218.MathSciNetCrossRef
18.
E. Akin-Bohner, Y. Raffoul and C. Tisdell. Exponential Stability in Functional Dynamic Equations on Time Scales, Communications in Mathematical Analysis, Vol. 9, N. 1, pp. 93–108(2010).
19.
E. Akin-Bohner, M. Bohner and F. Akin. Pachpatte Inequalities on Time Scales, Journal of Inequalities in Pure and Applied Mathematics, vol. 6, no. 1, article 6, pp. 1–23, 2005.
20.
S. Althubiti, H. A. Makhzoum and Y. N. Raffoul. Periodic Solution and Stability in Nonlinear Neutral System with Infinite Delay, Appl. Math. Sci. 7(136) (2013), 6749–6764.MathSciNet
21.
P. Amster, C. Rogers and C.C. Tisdell. Existence of Solutions to Boundary Value Problems for Dynamic Systems on Time Scales, J. Math. Anal. Appl. 308 (2005), 565–577.MathSciNetCrossRef
22.
D. Anderson. Global Stability for Nonlinear Dynamic Equations with Variable Coefficients, J. Math. Anal. Appl., 345(2008), pp. 796–804.MathSciNetCrossRef
23.
A. Anokhin, L. Berezansky and E. Braverman. Exponential Stability of Linear Delay Impulsive Differential Equations, J. Math. Anal. Appl. 193(1995) 923–991.MathSciNetCrossRef
Metadata
Title
Oscillations of First-Order Functional Dynamic Equations
Author
Svetlin G. Georgiev
Copyright Year
2019
Book
Functional Dynamic Equations on Time Scales

Print ISBN: 978-3-030-15419-6

Electronic ISBN: 978-3-030-15420-2

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-15420-2_6

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