Stability criteria for certain third-order delay differential equations

On Oscillation Criteria for Third Order Nonlinear Delay Differential Equations

In this paper we are concerned with the oscillation of third order nonlinear delay differential equations of the form ( r2 (t) ( r1 (t)x′ )′)′ + p (t)x′ + q (t) f (x (g (t))) = 0. We establish some new sufficient conditions which insure that every solution of this equation either oscillates or converges to zero.

Oscillation criteria for third-order delay differential equations

By a solution of (.) wemean a function y(t) ∈ C[ty,∞) which has the property r(t)y′(t) ∈ C[ty,∞) and r(t)(r(t)y′(t))′ ∈ C[ty,∞) and satisfies (.) on [ty,∞) for every t ≥ ty ≥ t. We restrict our attention to those solutions of (.) which exist on I and satisfy the condition sup{|x(t)| : t ≥ t} >  for any t ≥ ty. We assume that (.) possesses such a solution. A solution y(t) of (...

On the Stability of Solutions of Certain Non-Linear Third-Order Delay Differential Equations

In this paper, we study equation (1.6) and (1.7) and establish some sufficient conditions for the asymptotic stability of the zero solution of them.

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

Oscillation Criteria for Certain Third Order Nonlinear Difference Equations

Some new criteria for the oscillation of all solutions of third order nonlinear difference equations of the form ∆ a(n)(∆ 2 x(n)) α + q(n)f (x[g(n)]) = 0 and ∆ a(n)(∆ 2 x(n)) α = q(n)f (x[g(n)]) + p(n)h(x[σ(n)]) with ∞ a −1/α (n) < ∞ are established.