Nonoscillatory solutions of higher order differential equations

Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions

The continuability, boundedness, monotonicity, and asymptotic properties of nonoscillatory solutions for a class of second-order nonlinear differential equations p t h x t f x′ t ′ q t g x t are discussed without monotonicity assumption for function g. It is proved that all solutions can be extended to infinity, are eventually monotonic, and can be classified into disjoint classes that are full...

Nonoscillatory Solutions of Second Order Differential Equations with Integrable Coefficients

The asymptotic behavior of nonoscillatory solutions of the equation x" + a{t)\x\' sgnx = 0, y > 0 , is discussed under the condition that A(t) = limr_00/, a(s)ds exists and A(t) > 0 for all t. For the sublinear case of 0 < y < 1 , the existence of at least one nonoscillatory solution is completely characterized.

Bounded Nonoscillatory Solutions for First Order Neutral Delay Differential Equations

This paper deals with the first order neutral delay differential equation (x(t) + a(t)x(t− τ))′ + p(t)f(x(t− α)) +q(t)g(x(t − β)) = 0, t ≥ t0, Using the Banach fixed point theorem, we show the existence of a bounded nonoscillatory positive solution for the equation. Three nontrivial examples are given to illustrate our results. Mathematics Subject Classification: 34K4

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...

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