Existence of Nonoscillatory Solution of Second Order Linear Neutral Delay Equation

Existence of Nonoscillatory Solution of Third Order Linear Neutral Delay Difference Equation with Positive and Negative Coefficients

Abstract: In this paper, by using fixed point theorem, the problem of existence of the nonoscillatory solution for a class of neutral delay difference equations with both positive and negative coefficients has been investigated. Under the assumption of third order, a sufficient condition is proposed for the existence of the nonoscillatory solution. Further studies on the underlying problem have...

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...

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...

Existence of Nonoscillatory Solutions to Second-Order Neutral Delay Dynamic Equations on Time Scales

Linear Perturbations of a Nonoscillatory Second Order Differential Equation Ii

Let y1 and y2 be principal and nonprincipal solutions of the nonoscillatory differential equation (r(t)y′)′ + f(t)y = 0. In an earlier paper we showed that if ∫∞(f − g)y1y2 dt converges (perhaps conditionally), and a related improper integral converges absolutely and sufficently rapidly, then the differential equation (r(t)x′)′ + g(t)x = 0 has solutions x1 and x2 that behave asymptotically like...