[PDF] Top 20 Oscillation Criteria for Second Order Neutral Delay Dynamic Equations with Mixed Nonlinearities

... where γ > 0 is a quotient of odd positive integers, r t, qt are positive real valued rd- continuous functions on T, pt is a nonnegative real valued rd-continuous function on T and established sufficient conditions for ... See full document

... the oscillation of equations of mixed type is necessary as such equations arise in mathematical modeling, for example, in the growth of bacteria population with competitive ...general ... See full document

... The natural question now is: Can one obtain new oscillation criteria for (.) that improve the results in [, , , , ]? The aim of this paper is to give an affirmative answer to this question. As a ... See full document

... Remark . In this paper, several new oscillation criteria for equation (.) are obtained by using the Riccati substitution and Bernoulli’s inequality. Employing inequalities differ- ent from those ... See full document

... “Oscillation Criteria for Forced Second Order Quasi-Linear Differential Equations,” Ma- thematical and Computer Modelling, ...“Oscillation Criteria for ... See full document

... to dynamic equations on time scales, or mea- sure chains, and we refer the reader to the landmark paper of Hilger [] for a comprehen- sive treatment of the ...the oscillation and ... See full document

... The purpose of this paper is to obtain a new sufficient condition for oscillation of (.). The result obtained is essentially new for equations (.)-(.). This paper is organized as follows. In Section , ... See full document

... The theory of time scales, which has recently received a lot of attention, was introduced by Hilger in his Ph.D. thesis in 1988 in order to unify continuous and discrete analysis (see Hilger [1]). Several authors ... See full document

... Equations of this type arise in a number of important applications such as problems in population dynamics when maturation and gestation are included, in cobweb mod- els, in economics where demand depends on the ... See full document

... φt, t, l 0, φt, l, l 0, and φt, s, l > 0, for l < s < t, and has the partial derivative ∂φ/∂s on E such that ∂φ/∂s is locally integrable with respect to s in E. By choosing the special function φ, it is possible ... See full document

... Saker, Asymptotic Behavior of Solutions of a Third-Order Non-linear Dynamic Equation on Time Scales, Journal of Computational and Applied Mathematics 181, (2005) 92-102. Thandapani, O[r] ... See full document

... On the Oscillation of Second-Order Nonlinear Neutral Delay Dynamic Equations on Time Scales Quanxin Zhang, Xia Song, Li Gao Department of Mathematics, Binzhou University, Shandong, China[r] ... See full document

... This paper is concerned with oscillation and asymptotic behavior of a second-order neutral delay dynamic equation on an arbitrary time scale. We obtain two theorems which ... See full document

... new oscillation criteria for the second-order nonlinear delay dynamic equations on time ...the oscillation of the second-order nonlinear delay ... See full document

... of dynamic equations on time scales, which goes back to Hilger [], provides a rapidly expanding body of literature where the main idea is to unify, extend, and generalise concepts from continuous, discrete ... See full document

... difference equations can be applied in several fields such as bifurcation analysis, population dynamics, stability theory, the dynamics of delayed network systems and ...of neutral delay difference ... See full document

... differential equations is an important branch of differential ...the oscillation theory of impulsive differential equations emerging as an important area of research, since such equations have ... See full document

... interval oscillation criteria were recently extended to second-order dynamic equations in ...the second order nonlinear dynamic equations on time ... See full document

... A time scale T is an arbitrary nonempty closed subset of the real numbers. The theory of time scales was introduced by Hilger [6] in his Ph.D. thesis in 1988 in order to unify continuous and discrete analysis. ... See full document

... difference equations, and dynamic equations on time scales have an enor- mous potential for applications in biology, engineering, economics, physics, neural net- works, social sciences, ...of ... See full document