On the Oscillation of Third Order Half-linear Neutral Type Difference Equations
نویسندگان
چکیده
where α > 0, qn ≥ 0, 0 ≤ pn ≤ p < ∞. By using Riccati transformation we establish some new sufficient conditions which ensure that every solution of equation (E) is either oscillatory or converges to zero. These results improve some known results in the literature. Examples are provided to illustrate the main results. 2000 AMS Subjects Classification: 39A10
منابع مشابه
Oscillation Results for Third Order Half-linear Neutral Difference Equations
In this paper some new sufficient conditions for the oscillation of solutions of the third order half-linear difference equations ∆ ( an(∆ (xn + bnh(xn−δ))) α ) + qnf(xn+1−τ ) = 0 and ∆ ( an(∆ (xn − bnh(xn−δ))) α ) + qnf(xn+1−τ ) = 0 are established. Some examples are presented to illustrate the main results.
متن کاملOn the Oscillation of Solutions of Third Order Linear Difference Equations of Neutral Type
In this note we consider the third order linear difference equations of neutral type (E) ∆[x(n)− p(n)x(σ(n))] + δq(n)x(τ (n)) = 0, n ∈ N(n0), where δ = ±1, p, q : N(n0) → + ; σ, τ : N(n0) → , lim n→∞ σ(n) = lim n→∞ τ (n) = ∞. We examine the following two cases: {0 < p(n) 6 1, σ(n) = n + k, τ (n) = n + l}, {p(n) > 1, σ(n) = n − k, τ (n) = n − l}, where k, l are positive integers and we obtain su...
متن کاملNonlinear oscillation of certain third-order neutral differential equation with distributed delay
The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...
متن کاملOscillation constants for half-linear difference equations with coefficients having mean values
We investigate second order half-linear Euler type difference equations whose coefficients have mean values. We show that these equations are conditionally oscillatory and we explicitly identify the corresponding oscillation constants given by the coefficients. Our results generalize the known ones concerning equations with positive constant, periodic, or (asymptotically) almost periodic coeffi...
متن کاملOscillation of Second-Order Neutral Dynamic Equations with Mixed Arguments
We present some new oscillation criteria for a class of half-linear second-order neutral dynamic equations with mixed arguments. An example is given to illustrate the main results.
متن کامل