[PDF] Top 20 Dynamical Properties in a Fourth Order Nonlinear Difference Equation

... In this paper, it is of key for us to find that the lengths of positive and negative semi- cycles of nontrivial solutions of 1.1 occur periodically with prime period 15 with the rule 4 , 3 − , 1 , 2 − , 2 , 1 − , 1 , 1 − ... See full document

... difference equation, as a kind of typical nonlinear difference equations, is always a subject studied in recent ...of nonlinear difference equations of order greater than one come from the ... See full document

... of equation (1) is called oscillatory if for any m ∈N there exist m, m2 ≥ m such that x(m1)x(m2) <0, otherwise it is non ...oscillatory. equation (1) is called B-oscillatory if all its bounded solutions ... See full document

... (NLS) equation is one of the most important equations of mathematical physics with applications in many fields [1–4] such as plasma physics, nonlinear optics, water waves, and bimolecular ...NLS ... See full document

... There are quite a lot of numerical studies for the classical GLE and FGLE, see [7–15] and the references therein. To the authors’ best knowledge, there are not too many numerical studies for the CFGLE. As far as we are ... See full document

... nodal properties of ...nodal properties of so- lutions of the problem as a topological property and to get these solutions by means of a variational principle with two ... See full document

... Schrödinger equation (FNLS) was derived from the Lévy path in- tegrals instead of the Brownian path integrals as done in the classical Schrödinger equa- tion given by Feynman and Hibbs ... See full document

... of nonlinear difference equation was studied intensively by ...of nonlinear neutral delay difference ...the fourth order nonlinear neutral delay difference ... See full document

... (ii) Oscillation criteria established in [] are based on a different approach than that ap- plied here, namely by comparing () with certain first- and second-order difference equa- tions whose oscillatory ... See full document

... In this work we study various properties of (.). In Section  we study attractivity, stabil- ity and attractive region of (.) and its related equations. Further more we study bifurca- tions of (.). In ... See full document

... a nonlinear equation instead of a rational difference equation one ...of nonlinear difference equations of order greater than ...qualitative properties of ... See full document

... In the last few years there has been an increasing interest in the study of oscillatory and asymptotic behavior of solutions of difference equations. Compared to second-order difference equations, the study of ... See full document

... It is well known that difference equations appear naturally as discrete analogs and as nu- merical solutions of differential equations and delay differential equations having many applications in economics, biology, ... See full document

... Proof We must prove that the positive equilibrium point x ¯ of Equation (1.1) is both locally asymptotically stable and globally attractive. Theorem 3.5 has shown the local asymptotic stability of x. Hence, it ... See full document

... Sun, “Existence of a solution and a positive solution of a boundary value problem for a nonlinear fourth-order dynamic equation,” Nonlinear Analysis: Theory, Methods & Applications ,[r] ... See full document

... Motivated by the above works, in the present paper we study the existence of infinitely many solutions for problem (.) when the nonlinear term f (x, u) satisfies the superlinear condition and sublinear condition ... 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

... Remark . Notice that equation (.) does not imply the existence of L [u]() nor L [u](L). However, the fact of L [u] = v almost everywhere, joined with condition (.), is enough to guarantee that (.) makes ... See full document

... Remark . When mass-critical nonlinearity and nonlinearity with derivative appear at the same time, nonlinearity with second-order derivative plays more important role. This property is consistent with the ... See full document

... the nonlinear difference equation in the title, that is, the global asymptotical stability of zero equilibrium, the existence of unbounded solutions, the existence of period two solutions, the existence of ... See full document