[PDF] Top 20 Positive periodic solutions of second order difference equations with weak singularities

... where c Î C( ℝ , ℝ ) is T-periodic. They proved that for l ≥ 1 (called strong force con- dition in a terminology first introduced by Gordon [8,9]), a necessary and sufficient condition for the existence of a ... See full document

... of positive measure, the singularity may combine attractive and repulsive ...are positive constants, the singular term can be re- garded as a generalized Lennard-Jones force or van der Waals ... See full document

... a weak singularity can play an important role if Schauder’s fixed point theorem is chosen in the proof of the existence of positive periodic solutions for ...is positive in a set of ... See full document

... of periodic solutions to difference systems, which are globally superquadratic or ...of periodic solutions to autonomous ...of periodic solutions with prescribed minimal period to ... 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

... Differential equations with piecewise constant argument, which were firstly considered by Cooke and Wiener 1, and Shah and Wiener 2, usually describe hybrid dynamical systems a combination of continuous and ... See full document

... Our first theorem is devoted to the existence of asymptotically constant solutions which are positive and monotone increasing, hence nonoscillatory. It is a discrete counterpart of recent results by Dub´e ... See full document

... of periodic solution is studied for p-Laplacian Liénard equations with singular at x = 0 and x = ...of second order differential equations with ... See full document

... We obtain a sufficient condition for the existence of periodic and subharmonic solutions of second-order p-Laplacian di ff erence equations using the critical point theory. Copyright © ... See full document

... For the second-order equation 1.1 , we have the following theorem which provides new information about the decreasing fast solutions obtained by Aprahamian et al. 1. Theorem 1.4. Adopt the hypotheses ... 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

... differential equations has been a significant development in the last two ...decades. Periodic solutions and periodic boundary value problems of impulsive differential equations have ... 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

... is positive, it has been proved in [3] with e(x) ≡ 0 has at least one positive periodic solution when f (x, y) has a repulsive singu- larity near y = 0 and f (x, y) is superlinear near y = ... 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 ... See full document

... nontrivial periodic solutions of ...lower solutions [2, 10, 15], fixed point theorems [6, 7, 17–19], alternative principle of Leray–Schauder [4, 11], or topological degree theory [23, ...for ... 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 difference ... See full document

... where G(t, s) is the Green’s function associated to (1.2), see [7–13] for more details. Compared with the non-resonant problems, the research of resonant problems proceeds very slowly and the related results are few. ... See full document

... the periodic boundary value problems PBVPs for short for second-order ordinary or functional differential equations with or without impulse effects; see 1–24 and the references ... 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