Oscillation criteria for a second order damped difference equation

Oscillation criteria for nonlinear second-order difference equations with a nonlinear damped term

Sufficient conditions for the oscillation of solutions of the nonlinear second-order difference equation of the form [p(k)ψ(y(k)) y(k)] + q(k)h(y(k))g( y(k − r(k))) y(k) + f (k, y(k), y(k − s1(k)), y(k − s2(k)), . . . , y(k − sn(k))) = 0 are established. We obtain a series of results for oscillatory behaviour. © 2004 Elsevier Ltd. All rights reserved. MSC: 39A10

Annulus Criteria for Oscillation of Second Order Damped Elliptic Equations

Some annulus oscillation criteria are established for the second order damped elliptic differential equation N X i,j=1 Di[aij(x)Djy] + N X i=1 bi(x)Diy + C(x, y) = 0 under quite general assumption that they are based on the information only on a sequence of annuluses of Ω(r0) rather than on the whole exterior domain Ω(r0). Our results are extensions of those due to Kong for ordinary differentia...

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 ...

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

Oscillation criteria for second-order linear difference equations

A non-trivial solution of (1) is called oscillatory if for every N > 0 there exists an n > N such that X,X n + , 6 0. If one non-trivial solution of (1) is oscillatory then, by virtue of Sturm’s separation theorem for difference equations (see, e.g., [S]), all non-trivial solutions are oscillatory, so, in studying the question of whether a solution {x,> of (1) is oscillatory, it is no restricti...