Interval criteria for second-order super-half-linear functional dynamic equations with delay and advance arguments

2010-01-01
Anderson, Douglas R.
Zafer, Ağacık
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.
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS

Suggestions

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...
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...
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.
Fibre products of Kummer covers and curves with many points
Özbudak, Ferruh (Springer Science and Business Media LLC, 2007-10-01)
We study the general fibre product of any two Kummer covers of the projective line over finite fields. Under some assumptions, we obtain an involved condition for the existence of rational points in the fibre product over a rational point of the projective line so that we determine the exact number of the rational points. Using this, we construct explicit examples of such fibre products with many rational points. In particular we obtain a record and a new entry for the table (http://www.science.uva.nl/(simi...
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.
Citation Formats
D. R. Anderson and A. Zafer, “Interval criteria for second-order super-half-linear functional dynamic equations with delay and advance arguments,” JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, pp. 917–930, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/56843.