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Full-Text Articles in Mathematics
Oscillation Of Second-Order Half-Linear Neutral Noncanonical Dynamic Equations, Martin Bohner, Hassan El-Morshedy, Said Grace, Irena Jadlovská
Oscillation Of Second-Order Half-Linear Neutral Noncanonical Dynamic Equations, Martin Bohner, Hassan El-Morshedy, Said Grace, Irena Jadlovská
Mathematics and Statistics Faculty Research & Creative Works
In This Paper, We Shall Establish Some New Criteria for the Oscillation of Certain Second-Order Noncanonical Dynamic Equations with a Sublinear Neutral Term. This Task is Accomplished by Reducing the Involved Nonlinear Dynamic Equation to a Second-Order Linear Dynamic Inequality. We Also Establish Some New Oscillation Theorems Involving Certain Integral Conditions. Three Examples, Illustrating Our Results, Are Presented. Our Results Generalize Results for Corresponding Differential and Difference Equations.
Delay Dynamic Equations On Isolated Time Scales And The Relevance Of One-Periodic Coefficients, Martin Bohner, Tom Cuchta, Sabrina Streipert
Delay Dynamic Equations On Isolated Time Scales And The Relevance Of One-Periodic Coefficients, Martin Bohner, Tom Cuchta, Sabrina Streipert
Mathematics and Statistics Faculty Research & Creative Works
We are motivated by the idea that certain properties of delay differential and difference equations with constant coefficients arise as a consequence of their one-periodic nature. We apply the recently introduced definition of periodicity for arbitrary isolated time scales to linear delay dynamic equations and a class of nonlinear delay dynamic equations. Utilizing a derived identity of higher order delta derivatives and delay terms, we rewrite the considered linear and nonlinear delayed dynamic equations with one-periodic coefficients as a linear autonomous dynamic system with constant matrix. As the simplification of a constant matrix is only obtained for one-periodic coefficients, dynamic …
Asymptotic Properties Of Kneser Solutions To Third-Order Delay Differential Equations, Martin Bohner, John R. Graef, Irena Jadlovská
Asymptotic Properties Of Kneser Solutions To Third-Order Delay Differential Equations, Martin Bohner, John R. Graef, Irena Jadlovská
Mathematics and Statistics Faculty Research & Creative Works
The aim of this paper is to extend and complete the recent work by Graef et al. (J. Appl. Anal. Comput., 2021) analyzing the asymptotic properties of solutions to third-order linear delay differential equations. Most importantly, the authors tackle a particularly challenging problem of obtaining lower estimates for Kneser-type solutions. This allows improvement of existing conditions for the nonexistence of such solutions. As a result, a new criterion for oscillation of all solutions of the equation studied is established.
Oscillation Criteria For Third-Order Functional Differential Equations With Damping, Martin Bohner, Said R. Grace, Irena Jadlovska
Oscillation Criteria For Third-Order Functional Differential Equations With Damping, Martin Bohner, Said R. Grace, Irena Jadlovska
Mathematics and Statistics Faculty Research & Creative Works
This paper is a continuation of the recent study by Bohner et al [9] on oscillation properties of nonlinear third order functional differential equation under the assumption that the second order differential equation is nonoscillatory. We consider both the delayed and advanced case of the studied equation. The presented results correct and extend earlier ones. Several illustrative examples are included.
Oscillation Criteria For Fourth Order Nonlinear Positive Delay Differential Equations With A Middle Term, Said R. Grace, Elvan Akin
Oscillation Criteria For Fourth Order Nonlinear Positive Delay Differential Equations With A Middle Term, Said R. Grace, Elvan Akin
Mathematics and Statistics Faculty Research & Creative Works
In this article, we establish some new criteria for the oscillation of fourth order nonlinear delay differential equations of the form (Equation presented) provided that the second order equation (Equation presented) is nonoscillatiory or oscillatory. This equation with g(t) = t is considered in [8] and some oscillation criteria for this equation via certain energy functions are established. Here, we continue the study on the oscillatory behavior of this equation via some inequalities.