Nonlinear relationships between oscillation and asymptotic behavior

Oscillation and Asymptotic Behavior of Higher-Order Nonlinear Differential Equations

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Oscillation and Asymptotic Behavior of Solutions of Certain Third-Order Nonlinear Delay Dynamic Equations

The paper deals with the oscillation and asymptotic behavior of solutions of the third-order nonlinear delay dynamic equation { b(t) ([ a(t) ( x(t) )α]∆ )β}∆ + f(t, x(τ(t))) = 0 on a time scale T, where α, β > 0 are quotients of odd positive integers. We obtain some sufficient conditions which ensure that every solution of the equation either oscillates or converges to zero. Our results extend ...

Oscillation and Asymptotic Behavior of Solutions of Nth Order Nonlinear Delay Differential Equations*

where n >, 2, a: [0, 00) + [0, a~), q: [0, co) --+ (-00, co), andf: (--co, 03) + (-00, CQ). We assume a(l), q(t), andf( x are continuous, q(t) < t for all t > 0, q(t) 3 co ) as t ---f co, and xf(x) > 0 for x # 0. Usually, a condition of monotonicity on f is needed in order to obtain results for Eq. (1) analogous to those of an ordinary differential equation of the same type. Many authors observ...

Oscillation and Asymptotic Behavior of a Third-order Nonlinear Dynamic Equation

In this paper we establish some new oscillation criteria for the third-order nonlinear dynamic equation (c(t) ( (a(t)x(t)) )γ ) + f(t, x(t)) = 0, t ∈ [a,∞)T on time scales, where γ ≥ 1 is a quotient of odd integers. Our results not only unify the oscillation theory for third-order nonlinear differential and difference equations but also are new for the q-difference equations and can be applied ...