Nonoscillatory solutions of neutral dynamic equations with positive and negative coefficients on time scales

Existence of Nonoscillatory and Oscillatory Solutions of Neutral Differential Equations with Positive and Negative Coefficients

In this paper, we study the existence of oscillatory and nonoscillatory solutions of neutral differential equations of the form ( x(t)− cx(t− r))′ ± (P (t)x(t− θ)−Q(t)x(t− δ)) = 0 where c > 0, r > 0, θ > δ 0 are constants, and P , Q ∈ C( +, +). We obtain some sufficient and some necessary conditions for the existence of bounded and unbounded positive solutions, as well as some sufficient condit...

Existence of nonoscillatory solutions of higher-order neutral differential equations with positive and negative coefficients

Throughout this paper, the following conditions are assumed to hold. () n≥  is a positive integer, r ∈ C([t,∞),R+),  < a < b, τ > , σ > ; () p ∈ C([t,∞)× [a,b],R), q ∈ C([t,∞),R+), q ∈ C([t,∞),R+), h ∈ C([t,∞),R); () (u) is a continuously increasing real function with respect to u defined on R, and –(u) satisfies the local Lipschitz condition; () gi ∈ C(R,R), gi(u) satisfy the l...

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

Nonoscillatory Solutions to Forced Higher-order Nonlinear Neutral Dynamic Equations on Time Scales

By employing Kranoselskii’s fixed point theorem, we obtain sufficient conditions for the existence of nonoscillatory solutions of the forced higher-order nonlinear neutral dynamic equation [x(t) + p(t)x(τ(t))]∇ m + k ∑ i=1 pi(t)fi(x(τi(t))) = q(t) on a time scale, where pi(t), fi(t) and q(t) may be oscillatory. Then we establish sufficient and necessary conditions for the existence of nonoscill...

Nonoscillatory Solutions for System of Neutral Dynamic Equations on Time Scales

We will discuss nonoscillatory solutions to the n-dimensional functional system of neutral type dynamic equations on time scales. We will establish some sufficient conditions for nonoscillatory solutions with the property lim(t → ∞) x(i) (t) = 0, i = 1, 2,…, n.