OSCILLATION CRITERIA FOR SECOND ORDER LINEAR GENERALIZED DIFFERENCE EQUATION

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...

Integral Criteria for Second-Order Linear Oscillation

We present several new criteria for the oscillation of the second-order linear equation y(t) + q(t)y(t) = 0, in which the coefficient q may or may not change signs. The criteria involve the integral ∫ tq(t) dt for some γ > 0. The special case γ = 2 is then studied in greater details. AMS Subject Classification: 34C10

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 Differential Equations^)

where p(x) is a continuous positive function for 0<x< oo. Equation (1) is said to be nonoscillatory in (a, oo) if no solution of (1) vanishes more than once in this interval. Because of the Sturm separation theorem, this is equivalent to the existence of a solution which does not vanish at all in (a, oo). The equation will be called nonoscillatory—without the interval being mentioned —if there ...