Forced second order nonlinear oscillation

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 theorems for second order nonlinear forced differential equations

In this paper, a class of second order forced nonlinear differential equation is considered and several new oscillation theorems are obtained. Our results generalize and improve those known ones in the literature.

Forced oscillation of second-order differential equations with mixed nonlinearities

where t ≥ t > , n ≥  is a natural number, βi ≥  (i = , , . . . ,n) are constants, r ∈ C([t,∞),R), qj, τj, e ∈ C([t,∞),R), r(t) > , r′(t)≥ , qj(t)≥  (j = , , , . . . ,n), e(t)≤ . We also assume that there exists a function τ ∈ C([t,∞),R) such that τ (t) ≤ τj(t) (j = , , , . . . ,n), τ (t)≤ t, limt→∞ τ (t) =∞, and τ ′(t) > . We consider only those solutions x of equation (....

Oscillation of Forced Second Order Dynamic Equations on Time Scales

In this paper, by introducing a nonnegative kernel function H(t, s), some oscillation criteria for a forced second-order dynamic equation on time scales are given. AMS Subject Classifications: 34K11, 34C10, 93C70.

Oscillation Theorems for Second-Order Forced Neutral Nonlinear Differential Equations with Delayed Argument