[PDF] Top 20 Nonlocal type asymptotic behavior for solutions of second order difference equations

... Leray-Schauder type fixed point theorem, which states that a compact mapping T has a fixed point if it satisfies the Leray-Schauder boundary condition on B(, R), for some R > , that is, if there exists R >  ... See full document

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

... Therefore, all the solutions to the system (2.12) are oscillatory with respect to u = (1, 0) and with respect to v = (0, 1), that is, all the solutions to (2.12) have oscillating compo- nents. We wonder ... See full document

... 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

... investigation, asymptotic, oscillatory and bounded solutions of general second order difference equations under advanced setup, we come across specific conditions on the special ... See full document

... By a solution of (E) we mean a function x(t) : [T , ∞ ) → R , T ≥ a which is continuously differentiable together with p(t)ϕ(x (t)) on [T , ∞ ) and satisfies (E) at every point of [T, ∞ ). It is easily seen (see []) that ... See full document

... In , Saker et al. [] posed an open problem as follows: How to establish oscillation criteria for equation (.) when condition (.) holds? Assuming (.), Zhang et al. [, ] obtained some sufficient conditions ... See full document

... for solutions to a special summation equation and a first order nonlinear difference equation which will be often used ...for asymptotic solutions of second-order linear difference ... See full document

... of solutions for differential-difference equations, that is, continuous in space and discrete in time, has been the subject of in- creasing interest in the last ... See full document

... the asymptotic properties of the solutions of second order differential equations [1] [2] difference equ- ations of the type (E) and/or related equations have been ... See full document

... of second order can arise during many applications in various scientific areas such as physics, biology, chemistry, biophysics, me- chanics, medicine, aerodynamics, economy, atomic energy, control theory, ... See full document

... and asymptotic behavior of solutions of neutral difference equations, see [1]-[5], and the references cited ...and asymptotic behavior of solu- tions of neutral ... 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

... and asymptotic behavior results for a class of third-order nonlinear neutral dynamic equations on time scales are ...dynamic equations of the type considered ... See full document

... an asymptotic formula for these solutions to () with n =  (see []) and sup- posed all such solutions to have power asymptotic behavior for other n, ...such solutions behave ... See full document

... difference equations with many examples in applications such as asymptotic behavior of solutions of difference equations were studied extensively by Elaydi [] where the analytic and ... See full document

... of second order difference of any two linear combination of a given ...the asymptotic behavior of sequence under suitable combination of second order functional ...even ... See full document

... By a symmetry argument, one has that x m is also a solution to 4.8. By inspection of the coefficients of the polynomial in the left-hand side of 4.8 one sees that two positive solutions are possible only when q < ... See full document

... [10] N. C. Apreutesei, “Second-order differential equations on half-line associated with monotone operators,” Journal of Mathematical Analysis and Applications, vol. 223, no. 2, pp. 472–493, 1998. ... See full document