Oscillation of Second-Order Mixed-Nonlinear Delay Dynamic Equations

Download

index.pdf

Date

2010-01-01

Author

Unal, M.
Zafer, Ağacık

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

156
views

0
downloads

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.

Subject Keywords

Algebra and Number Theory, Applied Mathematics, Analysis

URI

https://hdl.handle.net/11511/57711

Journal

ADVANCES IN DIFFERENCE EQUATIONS

DOI

https://doi.org/10.1155/2010/389109

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 Criteria for Second-Order Forced Dynamic Equations with Mixed Nonlinearities Agarwal, Ravi P.; Zafer, A. (Springer Science and Business Media LLC, 2009) 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 contin...
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.
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.
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

M. Unal and A. Zafer, “Oscillation of Second-Order Mixed-Nonlinear Delay Dynamic Equations,” ADVANCES IN DIFFERENCE EQUATIONS, pp. 0–0, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/57711.