Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Oscillation Criteria for Second-Order Forced Dynamic Equations with Mixed Nonlinearities
Download
938706.pdf
Date
2009
Author
Agarwal, Ravi P.
Zafer, A.
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
63
views
52
downloads
Cite This
We obtain new oscillation criteria for second-order forced dynamic equations on time scales containing mixed nonlinearities of the form (r(t)Phi(alpha)(x(Delta)))(Delta) + f(t,x(sigma)) = e(t), t is an element of [t(0), infinity)(T) with f (t, x) = q(t) Phi(alpha)(x) + Sigma(n)(i=1)q(i)(t)Phi(beta i)(x), Phi(*)(u) = vertical bar u vertical bar*(-1) u, where [t(0), infinity)(T) is a time scale interval with t(0) is an element of T, the functions r, q, q(i), e : [t(0), infinity)(T) -> R are right-dense continuous with r > 0, sigma is the forward jump operator, x(sigma) (t) := x(sigma(t)), and beta(1) > ... > beta(m) > alpha > beta(m+1) > ... beta(n) > 0. All results obtained are new even for T = R and T = Z. In the special case when T = R and alpha = 1 our theorems reduce to (Y. G. Sun and J. S. W. Wong, Journal of Mathematical Analysis and Applications. 337 (2007), 549-560). Therefore, our results in particular extend most of the related existing literature from the continuous case to arbitrary time scale. Copyright (C) 2009 R. P. Agarwal and A. Zafer.
Subject Keywords
Algebra and Number Theory
,
Applied Mathematics
,
Analysis
URI
https://hdl.handle.net/11511/50951
Journal
Advances in Difference Equations
DOI
https://doi.org/10.1155/2009/938706
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
Oscillation for a nonlinear dynamic system on time scales
Erbe, Lynn; Mert, Raziye (Informa UK Limited, 2011-01-01)
We study the oscillation properties of a system of two first-order nonlinear equations on time scales. This form includes the classical Emden-Fowler differential and difference equations and many of its extensions. We generalize some well-known results of Atkinson, Belohorec, Waltman, Hooker, Patula and others and also describe the relation to solutions of a delay-dynamic system.
Oscillation of nonlinear impulsive partial difference equations with continuous variables
Agarwal, R. P.; KARAKOÇ, FATMA; Zafer, Ağacık (Informa UK Limited, 2012-01-01)
By employing a difference inequality without impulses, we establish several sufficient conditions for the oscillation of solutions of a class of nonlinear impulsive partial difference equations with continuous variables.
Oscillation of Second-Order Mixed-Nonlinear Delay Dynamic Equations
Unal, M.; Zafer, Ağacık (Springer Science and Business Media LLC, 2010-01-01)
New oscillation criteria are established for second-order mixed-nonlinear delay dynamic equations on time scales by utilizing an interval averaging technique. No restriction is imposed on the coefficient functions and the forcing term to be nonnegative.
Interval criteria for second-order super-half-linear functional dynamic equations with delay and advance arguments
Anderson, Douglas R.; Zafer, Ağacık (Informa UK Limited, 2010-01-01)
Interval oscillation criteria are established for second-order forced super half-linear dynamic equations on time scales containing both delay and advance arguments, where the potentials and forcing term are allowed to change sign. Four discrete examples are provided to illustrate the relevance of the results. The theory can be applied to second-order dynamic equations regardless of the choice of delta or nabla derivatives.
Time scale extensions of a theorem of Wintner on systems with asymptotic equilibrium
Mert, R.; Zafer, Ağacık (Informa UK Limited, 2011-01-01)
Abstract We consider quasilinear dynamic systems of the form[image omitted]where is a time scale, and provide extensions of a theorem of Wintner on systems with asymptotic equilibrium to arbitrary time scales. More specifically, we give sufficient conditions for the asymptotic equilibrium of the above system in the sense that for any given constant vector c, there is a solution satisfying[image omitted] Our results are new for difference equations, q-difference equations and many other time scale systems ev...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
R. P. Agarwal and A. Zafer, “Oscillation Criteria for Second-Order Forced Dynamic Equations with Mixed Nonlinearities,”
Advances in Difference Equations
, pp. 1–20, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/50951.