Two-timing for forced oscillation equations

Oscillation of Volterra Integral Equations and Forced Functional Differential Equations

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(...

Forced Oscillation for Higher Order Functional Differential Equations

We establish some oscillation criteria for the solutions to forced higher-order differential equations. We do not assume that the forcing term is the n-th derivative of an oscillatory function, and do not assume that the coefficients are of a definite sign. Our results are illustrated with examples.

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.

Oscillation Criteria for First Order Forced Dynamic Equations

x(t) + r(t)Φγ (x σ (t)) + p(t)Φα (x σ (t)) + q(t)Φβ (x σ (t)) = f(t), with Φη (u) := |u| u, η > 0. Here r(t), p (t) , q(t) and f (t) are rdcontinuous functions on T and the forcing term f(t) is not required to be the derivative of an oscillatory function. Our results in the special cases when T = R and T = N involve and improve some previous oscillation results for first-order differential and ...