[PDF] Top 20 Oscillation criteria for difference equations with non monotone arguments

... Notation It is worth noting that the improvement of condition (.) to the corresponding condition (.) is significant, approximately .%, if we compare the values on the left- hand side of these conditions. Also, the ... See full document

... with q p/p − 1 being the conjugate number of p, and with a certain distinguished solution h of 1.7. This enables to apply the deeply developed linear oscillation theory when investi- gating oscillations of ... See full document

... Difference equations have attracted a great deal of attention of researchers in mathematics, biology, physics, and ...for oscillation of the solutions has been investigated ... 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

... This paper is organized as follows. In Section , we give general solutions of a discrete version of the Riemann-Weber generalization of Euler differential equation and decide an oscillation constant for the ... See full document

... where { c(n) } is a sequence of nonnegative real numbers and τ is any real number. In Section 3, we investigate the oscillatory property of (1.2) and discuss the case when λ = 1, that is, the linear case. Section 4 is ... See full document

... In Section 2, we present some preliminary lemmas and in Section 3, we establish some sufficient conditions which ensure that all solutions of equation (1.1) are either oscillatory or con[r] ... See full document

... of non-monotone arguments other than the pure mathematical interest, it approximates the natural phenomena described by equation of the type (E) or (E 0 ...view) monotone arguments ... See full document

... Candan Advances in Difference Equations 2013, 2013 112 http //www advancesindifferenceequations com/content/2013/1/112 R ES EA RCH Open Access Oscillation criteria for second order nonlinear neutral d[.] ... See full document

... discrete oscillation and conjucation of equation (1) will be based largely on a discrete version of the Riccati ...the oscillation of equation (1) is expressed in terms of the existence of a certain ... See full document

... We obtain some oscillation criteria for solutions of the nonlinear delay differ αj ence equation of the form xn+1 − xn + pn m j=1 xn−k = 0.. 2000 Mathematics Subject Classification.[r] ... See full document

... several non-monotone arguments and nonnegative coefficients is studied, and some new oscillation criteria are ...known criteria existing in the ... See full document

... difference equations has attracted many ...the oscillation and nonoscillation of solutions of delay difference ...a non-monotone or non-decreasing ... See full document

... 5. M. Maria Susai Manuel and G. Britto Antony Xavier, “Recessive, dominant and spiral behaviours of solutions of certain class of generalized difference equations”, International Journal of Differential ... See full document

... which contradicts (.). Thus, all solutions of (.) oscillate. As non-oscillation of (.) is equivalent to the existence of a positive or a negative solu- tion of the relevant differentiation ... See full document

... Zhang, Oscillation of first order linear differential equations with deviating arguments, Differential Integral Equations, 1 (1988), 305-314.. [9] N.[r] ... See full document

... In the following, we present some background details that motivate our research. Re- cently, Baculíková and Lacková [], Džurina and Hudáková [], Li et al. [, ], and Sun et al. [] established some ... See full document

... Differential equations with delayed and advanced arguments (also called mixed differential equations or equations with mixed arguments) occur in many problems of economy, biology and ... See full document

... Moreover, in view of Theorem ., it is an interesting problem to investigate equation . with non-monotone arguments and derive sufficient oscillation conditions, involving lim sup as co[r] ... See full document

... Under the assumption that the τ is non-monotone, we present sufficient conditions for the oscillation of first-order delay dynamic equations on time scales.. An example illustrating the [r] ... See full document