Tongxing Li

Oscillation and asymptotic behavior of third-order nonlinear retarded dynamic equations

This paper is concerned with oscillation and asymptotic behavior of a class of third-order nonlinear delay dynamic equations on an arbitrary time scale. A new theorem is presented that improves a number of results reported in the literature. Examples are included to illustrate new results.

On the oscillation of higher-order half-linear delay differential equations

Abstract In this note, we study the oscillatory behavior of the following higher-order half-linear delay differential equation ( r ( t ) ( x ( n − 1 ) ( t ) ) α ) ′ + q ( t ) x β ( τ ( t ) ) = 0 , t ≥ t 0 , where we assume ∫ t 0 ∞ 1 r 1 / α ( t ) d t ∞ . An example is given to illustrate the main results.

Oscillation Behavior of Third-Order Neutral Emden-Fowler Delay Dynamic Equations on Time Scales

We will establish some oscillation criteria for the third-order Emden-Fowler neutral delay dynamic equations on a time scale , where is a quotient of odd positive integers with , and real-valued positive rd-continuous functions defined on . To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study. Some examples are considered to illustrate the main results.

Oscillation of Even-Order Neutral Delay Differential Equations

By using Riccati transformation technique, we will establish some new oscillation criteria for the even order neutral delay differential equations , , where is even, , , and . These oscillation criteria, at least in some sense, complement and improve those of Zafer (1998) and Zhang et al. (2010). An example is considered to illustrate the main results.

Existence of Nonoscillatory Solutions to Second-Order Neutral Delay Dynamic Equations on Time Scales

We employ Kranoselskiis fixed point theorem to establish the existence of nonoscillatory solutions to the second-order neutral delay dynamic equation on a time scale T. To dwell upon the importance of our results, one interesting example is also included.

Oscillation for Second-Order Nonlinear Delay Dynamic Equations on Time Scales

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations on a time scale ; here is a quotient of odd positive integers with and real-valued positive rd-continuous functions defined on . Our results not only extend some results established by Hassan in 2008 but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation.

Oscillation results for fourth-order nonlinear dynamic equations

Abstract This work is concerned with the oscillation of a certain class of fourth-order nonlinear dynamic equations on time scales. A new oscillation result and an example are included.

Oscillation results for second-order neutral differential equations of mixed type

Abstract Some oscillation theorems are established for the second-order linear neutral differential equations of mixed type Several examples are also provided to illustrate the main results.

Oscillation of Third-Order Neutral Delay Differential Equations

The purpose of this paper is to examine oscillatory properties of the third-order neutral delay differential equation . Some oscillatory and asymptotic criteria are presented. These criteria improve and complement those results in the literature. Moreover, some examples are given to illustrate the main results.

Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations

Some oscillation criteria are established for the second-order superlinear neutral differential equations (𝑟(𝑡)|𝑧′(𝑡)|𝛼−1𝑧′(𝑡))′