[PDF] Top 20 Multiple periodic solutions for the second order nonlinear difference equations

... When δ = 1, equation (1) has been considered in [17] and [19]. When δ = 1 and ∇ F(n, x) = 0, equation (1) has been also studied. For example, in [1] and [8], the authors were interested in the results on disconjugacy, ... See full document

... of periodic solutions for the third-order differential equation ˙ x ¨ + ω 2 x ˙ = µF (x, x, ˙ x) ¨ is ...in order to reduce it to a second-order nonlinear differential ...of ... See full document

... when nonlinearity f is odd and resonant at infinity. Zheng and Xiao [] employed critical groups and the mountain pass theorem to study the existence of nontrivial solutions for (.) when the nonlinearity f (k, ... See full document

... has been aroused, where u(t) = u(t + ) – u(t),  u(t) = (u(t)), ∇F(t, x) = ∂F(t,x) ∂x , T is a positive integer, and Z and R denote the set of integers and the set of real numbers, respectively, and Z [a, b] = { a, a + ... See full document

... lower solutions and the cone expansion or the compression fixed point theorem, authors [, ] obtained the unique solution and positive solutions to the periodic difference ...ial solutions to ... See full document

... Compared to system (.), the neutral functional differential system (.) admits four control parameters p, q, λ, s. We aim to derive conditions in terms of these four control parameters for the existence and ... See full document

... of solutions for the problem are proved by means of the Leray-Schauder nonlinear alternative and some standard fixed point ...The nonlinear team f contains D q u(t) in the ... See full document

... Difference equations have attracted the interest of many researchers in the last 20 years since they provided a natural description of several discrete models, in which the periodic solution problem ... See full document

... This paper is divided into four parts. First of all, Section 2 states some basic notations and presents variational structure. Second, in Section 3, we shall state and prove our main results by using the ... See full document

... the following vector version of Krasnosel’skii’s fixed point theorem [14]. In addition, there are many papers concerned with the existence and multiplicity of radial solutions of the elliptic equations with ... See full document

... di¤erence equations or discrete dynamical systems are a fertile research area, not only in mathematics but also in many applied science such as economics, ...di¤erence equations or discrete dynamic systems ... See full document

... difference equations have been widely used to describe real-life situations in computer science, economics, neural network, ecology, cybernetics, ...of solutions to discrete ...of periodic ... See full document

... erential equations, which arise in physics, population dynamics, econom- ics, and so forth, are important mathematical tools for providing a better understanding of many real-world models, we refer to [1–5] and ... See full document

... oscillatory solutions for second-order nonlinear neutral delay difference equations are ...non-increasing solutions for corresponding first-order difference inequality, some ... See full document

... tions, e and g respectively denote the T -periodic and T -periodic in the first argument and T > . However, to the best of our knowledge, most authors mentioned above have only considered the existence ... See full document

... of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by(t + 1) + cy(t) = f (y(t)), where c = 0 and f : R → R is ...even multiple of ... See full document

... 0, n ∈ Z, 1.5 has been studied. Other interesting contributions can be found in some recent papers 7–11 and in references contained therein. It is interesting to study second-order nonlinear ... See full document

... for periodic solutions of a differential delay equation to the problem of finding periodic solutions for a related system of ordinary differential ...study periodic solutions of ... See full document

... Positive periodic solutions of second-order difference equations have been studied by many authors, see ...positive periodic solutions of the ... See full document

... where c ∈ R . Therefore, the periodic functions w and σ with properties (.) and (.) exist and, moreover, are unique up to a constant term, the value of which has no influence on the validity of the condition ... See full document