Nonoscillatory solutions of nonlinear differential systems

Classification of Nonoscillatory Solutions of Nonlinear Neutral Differential Equations

Nonoscillatory solutions of a general class of second order functional neutral differential equations of the form

Existence of Nonoscillatory Bounded Solutions for a System of Second-order Nonlinear Neutral Delay Differential Equations

A system of second-order nonlinear neutral delay differential equations ( r1(t) ( x1(t) + P1(t)x1(t− τ1) )′)′ = F1 ( t, x2(t− σ1), x2(t− σ2) ) , ( r2(t) ( x2(t) + P2(t)x2(t− τ2) )′)′ = F2 ( t, x1(t− σ1), x1(t− σ2) ) , where τi > 0, σ1, σ2 ≥ 0, ri ∈ C([t0,+∞),R), Pi(t) ∈ C([t0,+∞),R), Fi ∈ C([t0,+∞)× R2,R), i = 1, 2 is studied in this paper, and some sufficient conditions for existence of nonosc...

Asymptotic Decay of Nonoscillatory Solutions of General Nonlinear Difference Equations

The authors consider themth order nonlinear difference equations of the form Dmyn+qnf(yσ(n)) = ei, where m ≥ 1, n ∈N = {0,1,2, . . .}, an > 0 for i= 1,2, . . . ,m−1, an ≡ 1, D0yn = yn, Diyn = an∆Di−1yn, i = 1,2, . . . ,m, σ(n) → ∞ as n → ∞, and f : R → R is continuous with uf(u) > 0 for u = 0. They give sufficient conditions to ensure that all bounded nonoscillatory solutions tend to zero as n→...

Existence of Nonoscillatory Solutions for a Third-Order Nonlinear Neutral Delay Differential Equation

and Applied Analysis 3 Throughout this paper, we assume that R −∞, ∞ , R 0, ∞ , C t0, ∞ ,R denotes the Banach space of all continuous and bounded functions on t0, ∞ with the norm ‖x‖ supt≥t0 |x t | for each x ∈ C t0, ∞ ,R and A N,M {x ∈ C t0, ∞ ,R : N ≤ x t ≤ M, t ≥ t0} for M > N > 0. 1.8 It is easy to see that A N,M is a bounded closed and convex subset of C t0, ∞ ,R . By a solution of 1.7 , w...

On the Number of Zeros of Bounded Nonoscillatory Solutions to Higher-order Nonlinear Ordinary Differential Equations