[PDF] Top 20 On the asymptotic analysis of bounded solutions to nonlinear differential equations of second order

... Finally, when we look at ODEs (1)–(5), we see that ODEs (1)–(4) are linear and ODE (5) has a slightly modified nonlinear form. Next, ODEs (6) and (7) include and improve ODEs (1)–(4) from the linear cases to the ... 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

... 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

... functional differential equations have been studied in recent ...functional differential equations received much less attention, which is due mainly to the technical difficulties arising in ... See full document

... R n → R n , H ∈ C 0 ( R n ) and P ∈ C ( R n ) where C 0 ( R n ) is the set of all continuous function differentiable once on R n and C ( R n ) is the set of all continuous function on R n . Let R denote the real line −∞ ... See full document

... Recently, qualitative theory about the existence and stability of SDEs with jumps have been studied intensively for many scholars. For example, Applebaum [1-3], Li [16], Rong [31], Yin [38], Yang [39] and Zhu [40]. ... See full document

... of solutions of second order nonlinear neutral delay differential equations with positive and negative ...Differential Equations with ...Differential Equations with Deviating ... 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

... impulsive differential equations is an important branch of differential ...impulsive differential equations emerging as an important area of research, since such equations have ... See full document

... Onose, Asymptotic behavior of nonoscillatory solutions of functional differential equations of arbitrary order, J.. Onose, Nonoscillation theorems for differential equations with deviati[r] ... See full document

... Abstract. In this work, an attempt is made to discuss the existence of nonoscillatory solutions of second order nonlinear neutral differential equations with variable delays. The ... See full document

... of solutions to different functional differential equations, for some related contributions, we refer the reader to [–] and the references cited ...differential equations. Baculíková and Džurina [] ... See full document

... stability analysis as well as existence of periodic solutions of nonlinear ordinary differen- tial ...general, nonlinear dynamical systems exhibiting oscillating limit cycles can be found in a ... 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 of periodic ... See full document

... of differential equations such as (7) and (8) are said to be topologically equivalent in a neighborhood of the origin or to have the same qualitative structure near the origin if there is a homeomorphism Φ ... See full document

... Stability Implications on the Asymptotic Behavior of Second Order Differential Equations, Proc.. Stability and Asymptotic Behavior of Differential Equations, Heath, Boston, 1965.[r] ... See full document

... differential equations, see, for example, [2, 3, 1, 4, 5] and the references cited in ...the second-order nonlinear impulsive differential ... 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

... over (0,T ), by k · k the supremum norm of C[0, T ]. For a given function a ∈ L 1 [0, T ] essentially bounded, we denote the essential supremum and infimum of a by a ∗ and a ∗ , respectively. Lemma 3.1 Assume Ω is ... See full document

... Examples In this section, we give some examples on our approach for reduction and finding solutions of nonlinear second order ordinary differential equations, these equations and more eq[r] ... See full document