Interval Oscillation Criteria for Second-Order Forced Functional Dynamic Equations on Time Scales

This paper is concerned with oscillation of second-order forced functional dynamic equations of the form (r(t)(xΔ(t))γ)Δ+∑i=0n‍qi(t)|x(δi(t))|αisgn  x(δi(t))=e(t) on time scales. By using a generalized Riccati technique and integral averaging techniques, we establish new oscillation criteria which handle some cases not covered by known criteria

OSCILLATION CRITERIA FOR SECOND ORDER FUNCTIONAL DYNAMIC EQUATIONS ON TIME-SCALES

Abstract: Using a Riccati transformation technique, the authors establish some new oscillation criteria for the second-order functional dynamic equation on a time scale T, where γ > 0 is a constant. The cases are both considered. Examples are provided to illustrate the relevance of the results

Oscillation of Second Order Nonlinear Dynamic Equations on Time Scales

By means of Riccati transformation techniques, we establish some oscillation criteria for a second order nonlinear dynamic equation on time scales in terms of the coefficients. We give examples of dynamic equations to which previously known oscillation criteria are not applicable

Oscillation theory for second order differential equations and dynamic equations on time scales

Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2004Includes bibliographical references (leaves. 55-57)Text in English; Abstract: Turkish and Englishvii, 57 leavesThis thesis provides the oscillation criteria for second order linear differential equations and dynamic equations on time scales. We establish the comparison theorems and oscillation criteria for selfadjoint and non-self adjoint equations and systems of first order ordinary differential equations. Then we prove the fundamental results concerning the dynamic equations: existence and uniqueness theorem and disconjugacy criteria

THEOREMS OF KIGURADZE-TYPE AND BELOHOREC-TYPE REVISITED ON TIME SCALES

This article concerns the oscillation of second-order nonlinear dynamic equations. By using generalized Riccati transformations, Kiguradzetype and Belohorec-type oscillation theorems are obtained on an arbitrary time scale. Our results cover those for differential equations and difference equations, and provide new oscillation criteria for irregular time scales. Some examples are given to illustrate our results

Forced oscillation of second order nonlinear dynamic equations on time scales

By means of the Kartsatos technique and generalized Riccati transformation techniques, we establish some new oscillation criteria for a second order nonlinear dynamic equations with forced term on time scales in terms of the coefficients

Asymptotic properties of solutions of certain third-order dynamic equations

AbstractIn this paper, the well known oscillation criteria due to Hille and Nehari for second-order linear differential equations will be generalized and extended to the third-order nonlinear dynamic equation (r2(t)((r1(t)xΔ(t))Δ)γ)Δ+q(t)f(x(t))=0 on time scale T, where γ≥1 is a ratio of odd positive integers. Our results are essentially new even for third-order differential and difference equations, i.e., when T=R and T=N. Two examples of dynamic equations on different time scales are given to show the applications of our main results