[PDF] Top 20 A classification scheme for nonoscillatory solutions of a higher order neutral difference equation

... results between our paper and [4–11], although some proofs are similar. However, the existence proofs are different in that Cheng-Patula existence theorem is applied in [7], monotone method is used in [10] while we use ... See full document

... of nonoscillatory or positive solutions of higher-order neutral differential equations was investigated in [–], but in this work our results contain not only exis- tence of ... See full document

... Let m  max    1 , 1  . A solution of the difference equation (1.1) is called eventually positive if there exists a positive integer n 0 such that x n    0 for n N n    0 . If there exists a ... See full document

... in terms of the Mountain Pass theorem relying on Ekeland’s variational principle and the diagonal method. Yu et al. [] established the existence of a periodic solution for equation (.) by means of the critical ... See full document

... for higher order nonlinear neutral difference equations which ensures that all the solutions are oscillatory when m is ...all solutions of ... See full document

... 8. Li, W.T., Cheng, S.S.: Oscillation criteria for a nonlinear difference equation. Comput. Math. Appl. 36, 87–94 (1998) 9. Liu, Z., Kang, S.M., Ume, J.S.: Existence of uncountably many bounded ... See full document

... contained therein. However, relatively few oscillation results are known for forced equations (see [5, 6, 7, 8, 9, 10, 11]). In this paper, we give sufficient conditions which ensure that all solutions of (1) are ... See full document

... positive solutions of ...positive solutions, but we also prove convergence and the error estimates of the Mann iterative algorithms relative to these positive ... See full document

... { , , . . . , n } . Shen and Debnath [] obtained some sufficient conditions for the oscilla- tions of (.) and Luo and Shen [] established a few oscillation and nonoscillation criteria for (.). Liu and Huang [] ... See full document

... Fourth-order non-neutral difference equations with one quasi-difference, by the tech- niques here used, were studied in [–]. Some generalizations of the results presented in these papers were published in ... See full document

... differential equation and difference equation has impor- tant academic value and application ...periodic solutions of neutral difference equations are relatively few (see [7, ... See full document

... in order to cre- ate a theory that can unify discrete and continuous analysis, which has received a lot of ...all solutions of an equation to be oscillatory has been a major focus of ...a ... See full document

... bounded solutions to many types of difference equation have been widely ...second order, see, for example, [–], and for higher orders, [–], and references ... See full document

... of neutral part in the discussed differential equations were all constant ...of higher-order neutral differential equations with distributed ... See full document

... the neutral part in the discussed differential equations were all constant delays, and the main thought in the employed verification method also was kept the same in which the coeffi- cient neutral part in the ... See full document

... Up to now there have been few studies on equations with continuously distributed delay on time scales. For some related works, the reader is referred to the papers [8–10]. In this paper, we obtain some new sufficient ... See full document

... Remark . In our paper, we consider the n-order period equation (.); in this sense, we generalize the model in [] to higher order under the equivalent conditions. Moreover, in view of the ... See full document

... Hindawi Publishing Corporation Advances in Difference Equations Volume 2009, Article ID 394635, 9 pages doi 10 1155/2009/394635 Research Article On a Conjecture for a Higher Order Rational Difference[.] ... See full document

... A Monthly Double-Blind Peer Reviewed Refereed Open Access International e-Journal - Included in the International Serial Directories International Journal in IT and Engineering.. http:/[r] ... 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 have ... See full document