[PDF] Top 20 On positive periodic solutions of second order difference equations with attractive repulsive singularities

... an attractive singularity, whereas ...a repulsive singularity. The interest in this type of equations began with the paper of Lazer and Solimini [], in which the authors provide necessary and ... See full document

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

... of periodic solutions for neutral differential equations has at- tracted the attention of many researchers; see [2–9, 14, 16–18, 20, 21] and the references cited ... See full document

... differential equations was paid to investigating the problem of periodic solutions for second order differential equations with ...the periodic problem for second ... See full document

... of positive periodic solutions to ...some equations like ...the equations have no T -periodic ...the periodic problem for some second-order differential ... See full document

... on periodic solutions for Duffing equations with a singularity (see [1–5, 7–11] and the references cited therein), in account of its applications in applied ...a positive π-periodic ... 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 ... See full document

... of periodic solutions for neutral differential equations with sin- gularity has been researched (see [7–9, ...a positive periodic solution of fourth-order neutral Liénard equation ... See full document

... is positive, absolutely continuous together with its first derivative, satisfies ...the repulsive case and/or when f has no ...of equations with a singular friction-like ... See full document

... 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

... denote the quasi-derivative of y(x), we call the periodic boundary conditions which are impor- tant representatives of nonseparated boundary conditions. The nonlinearity f ∈ C(( R /T Z ) × (0, ∞), R ). We are ... See full document

... which was initially studied by Lazer and Solimini []. They proved that for λ ≥  (called a strong force condition in the terminology first introduced by Gordon [, ]), a necessary and sufficient condition for the ... See full document

... a positive number β such that for all z > β, f (z) > 0 and f ( − z) < 0, (iii) when c = 1 and | b | < 2, then N arccos( − b/2) is not an even multiple of ... 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

... 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

... of positive doubly periodic solutions for a single regular tele- graph equation or regular telegraph system, see, for example, the papers [–] and the references ... See full document

... p-Laplacian-Liénard equations. We notice that all the restoring force terms in the equations studied by [, ] are not singular at x = ...of periodic solutions of the Liénard equation with a ... See full document

... x, y ≥ a n > 0, ∀ x, y ∈ X, with x, y = 0. (1.4) Unfortunately, this condition is extremely strong, since it implies that f (n, x) is in the ray { ax : a ≥ 0 } . A more convenient version of oscillation and condition ... See full document

... many periodic solutions to planar radially symmetric systems with certain strong repulsive singularities near the origin and with some semilinear growth near ... See full document

... Such equations have been studied by several authors including Cooke and Wiener [5, 6], Shah and Wiener [9], Aftabizadeh et ...such equations were motivated by the fact that they represent a hybrid of ... See full document