[PDF] Top 20 Oscillation results for difference equations with oscillating coefficients

... The following two examples illustrate that the conditions for oscillations (.) and (.) are independent. They are chosen in such a way that only one of them is satisfied. Also, in Example ., Theorem . [], ... See full document

... COMPARISON AND OSCILLATION RESULTS FOR DELAY DIFFERENCE EQUATIONS WITH OSCILLATING COEFFICIENTS WEIPING YAN and JURANG YAN.. Department of Mathematics Shanxi University Taiyuan,Shanxi 03[r] ... See full document

... The oscillation theory as a part of the qualitative theory of differential equations and difference equations has been developed rapidly in the last decades, and there have been many results on ... See full document

... The rest of the paper is organized as follows: Sect. 2 is devoted to the main results of the paper. We present our investigations in two folds for Eqs. (1) and (2). Meanwhile, a relevant result on the existence of ... See full document

... In Section 2, we present sufficient conditions which ensure that all solutions of equation (1.1) are either oscillatory or converges to zero, and we present similar results for equation (1.2) in Section 3. ... See full document

... the oscillation of ...the oscillation of ...the oscillation of (1.1) and employ the same techniques to obtain oscillation results for the neutral ... See full document

... typical results regarding ...difference equations of type (1.4;δ), the study of higher-order equations, and in particular third-order equations of type ...for equations with deviating ... See full document

... difference equations. We obtain some new results on the growth of meromorphic solutions when most coefficients in such equations are meromorphic functions, which are supplements of previous ... See full document

... which contradicts (). Therefore, this completes the proof. Remark . The results in this paper are of higher degree of generality. From Theo- rems .-., we can obtain many different sufficient conditions for ... See full document

... establish oscillation criteria of third-order nonlinear dynamic equations with nonpositive neutral coefficients on time scales by a generalized Riccati transformation and employing functions in some function ... See full document

... Remark  Our result is ‘backward compatible’ with previous results about the conditional oscillation of half-linear equations. More precisely, if the functions r and s in Eq. (.) are α-periodic ... See full document

... some oscillation criteria for the solutions of mth-order nonlinear neutral difference equation where m ≥ ...The results presented here complement some of the known results reported in the ... See full document

... difference equations with quasi-differences and deviating argument is ...new oscillation theorem for the sublinear case and we complete the existing results in the ... See full document

... conditional oscillation and we give a his- torical background of the ...considered equations together with the description of the used methods (the Riccati and Prüfer trans- ...lemmas, results, ... See full document

... the results obtained in the above mentioned papers to the q-fractional difference equations of the form ...the results obtained when the Riemann-Liouville q-differential operator is replaced by Caputo ... See full document

... Now we briefly explain why the oscillatory problems in the above examples are not cov- ered by any previously known results (see also Theorem ). In both of Examples  and , the second coefficient changes its sign. ... See full document

... use of the observation that if x(t) is an eventually positive solution of (1.1), then x (t) = p(t)x(t + τ) ≥ 0 for all large t so that x(t) is eventually nonde- creasing. However, when the coefficient p(t) is oscillatory, ... See full document

... difference equations has received much attention in recent years due to its extensive applications in computer, probability theory, queuing problems, sta- tistical problems, stochastic time series, combinatorial ... See full document

... differential equations presents com- plications and the results which are true for neutral differential equations may not be true for nonneutral differential ...differential equations has some ... See full document

... In this paper we study the oscillatory and nonoscillatory behavior of the solutions of certain third and fourth order difference equations.. Until recently, excepting the studies by Chen[r] ... See full document