Oscillation Criteria of Solution for a Second Order Difference Equation with Forced Term

Oscillation Criteria of Solution for a Second Order Difference Equation with Forced Term

Oscillation criteria for a forced second order nonlinear dynamic equation

In this paper, we will establish some new interval oscillation criteria for forced second-order nonlinear dynamic equation (p(t)x(t)) + q(t)|xσ(t)|γsgn x(t) = f(t), t ∈ [a, b], on a time scale T where γ ≥ 1. As a special case when T = R our results not only include the oscillation results for second-order differential equations established by Wong (J. Math. Anal. Appl., 231 (1999) 233-240) and ...

Interval Oscillation Criteria for Second Order Mixed Nonlinear Forced Impulsive Differential Equation with Damping Term

In this paper, interval oscillation criteria are established for second order forced impulsive differential equations with mixed nonlinearities of the form ⎧⎪⎨ ⎪⎩ ( r(t)Φα(x′(t)) )′ + p(t)Φα(x′(t))+q(t)Φα(x(t))+ n ∑ i=1 qi(t)Φβi (x(t)) = e(t), t = τk, x(τk) = akx(τk), x′(τk+) = bkx′(τk), k = 1,2, . . . . The results obtained in this paper extend some of the existing results and are illustrated ...

Oscillation criteria for first and second order forced difference equations with mixed nonlinearities

Some new criteria for the oscillation of certain difference equations with mixed nonlinearities are established. The main tool in the proofs is an inequality due to Hardy, Littlewood, and Pólya. c © 2006 Elsevier Ltd. All rights reserved.

Oscillation Criteria for First-order Forced Nonlinear Difference Equations

where (i) {p(n)}, {e(n)} are sequences of real numbers; (ii) {qi(n)}, i= 1,2, are sequences of positive real numbers; (iii) λ, μ are ratios of positive odd integers with 0 < μ < 1 and λ > 1. By a solution of equation (1, i), i= 1,2,3, we mean a nontrivial sequence {x(n)}which is defined for n ≥ n0 ∈ N = {0,1,2, . . .} and satisfies equation (1, i), i = 1,2,3, and n = 1,2, . . . . A solution {x(...