Shurong Sun

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.

Uniqueness of positive solutions for boundary value problems of singular fractional differential equations

In this article, we study the existence and uniqueness of a positive solution for the singular nonlinear fractional differential equation boundary value problem where 3u2009<u2009αu2009≤u20094 is a real number, is the Riemann–Liouville fractional derivative and f : (0,u20091]u2009×u2009[0,u2009+∞)u2009→u2009[0,u2009+∞) is continuous, (i.e. f is singular at tu2009=u20090). Our analysis relies on a fixed point theorem in partially ordered sets. As an application, an example is presented to illustrate the main results.

On the Oscillation of Second-Order Neutral Delay Differential Equations

Some new oscillation criteria for the second-order neutral delay differential equation , are established, where , , , . These oscillation criteria extend and improve some known results. An example is considered to illustrate the main results.

Existence of Positive Solutions for Multipoint Boundary Value Problem with p-Laplacian on Time Scales

We consider the existence of positive solutions for a class of second-order multi-point boundary value problem with -Laplacian on time scales. By using the well-known Krasnoselskis fixed-point theorem, some new existence criteria for positive solutions of the boundary value problem are presented. As an application, an example is given to illustrate the main results.

Oscillation Criteria for Second-Order Nonlinear Neutral Delay Differential Equations

Some sufficient conditions are established for the oscillation of second-order neutral differential equation , , where . The results complement and improve those of Grammatikopoulos et al. Ladas, A. Meimaridou, Oscillation of second-order neutral delay differential equations, Rat. Mat. 1 (1985), Grace and Lalli (1987), Ruan (1993), H. J. Li (1996), H. J. Li (1997), Xu and Xia (2008).

Oscillation for a Class of Second-Order Emden-Fowler Delay Dynamic Equations on Time Scales

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order Emden-Fowler delay dynamic equations on a time scale ; here is a quotient of odd positive integers with and as real-valued positive rd-continuous functions defined on . Our results in this paper not only extend the results given in Agarwal et al. (2005), Akin-Bohner et al. (2007) and Han et al. (2007) but also unify the results about oscillation of the second-order Emden-Fowler delay differential equation and the second-order Emden-Fowler delay difference equation.

Uniqueness of Periodic Solution for a Class of Liénard p-Laplacian Equations

By topological degree theory and some analysis skills, we consider a class of generalized Liénard type -Laplacian equations. Upon some suitable assumptions, the existence and uniqueness of periodic solutions for the generalized Liénard type -Laplacian differential equations are obtained. It is significant that the nonlinear term contains two variables.

Positive solutions for a coupled system of nonlinear differential equations of mixed fractional orders

AbstractIn this article, we study the existence of positive solutions for a coupled system of nonlinear differential equations of mixed fractional ordersn n where 2 < α ≤ 3, 3 < β ≤ 4, , are the standard Riemann-Liouville fractional derivative, and f, g : [0, 1] × [0, +∞) → [0, +∞) are given continuous functions, f(t, 0) ≡ 0, g(t, 0) ≡ 0. Our analysis relies on fixed point theorems on cones. Some sufficient conditions for the existence of at least one or two positive solutions for the boundary value problem are established. As an application, examples are presented to illustrate the main results.