Asymptotic and oscillatory behavior of solutions of a class of second order differential equations with deviating arguments

AbstractThe asymptotic and oscillatory behavior of solutions of damped nonlinear second order differential equations with deviating arguments of the type (a(t) ψ(x(t)) ẋ(t)). + p(t)ẋ(t) + q(t) + q(t)f(x[g(t)]) = 0 (. = d/dt) is studied. Criteria for oscillation of all solutions when the damping coefficient “p” is of constant sign on [t0, ∞) are established. Results on the asymptotic and oscillatory behavior of solutions of the damped-forced equation (a(t)ψ(x(t))ẋ(t)). + p(t)ẋ(t) + q(t)f(x[g(t)]) = e(t), where q is allowed to change signs in [t0, ∞), are also presented. Some of the results of this paper extend, improve, and correlate a number of existing criteria

Oscillation theorems for second order nonlinear functional differential equations with damping

AbstractNew oscillation criteria are given for a second order nonlinear functional differential equation (α(t)χ(t))′ + δp(t)χ′[σ(t)] − q(t)|χ[g(t)]|λ sgnχ[g(t)] = 0, where δ = ±1 and λ > 0

On oscillation of solutions of nth-order delay differential equations

AbstractOscillatory behavior of the solutions of the nth-order delay differential equation Lnx(t) + q(t)f(x[g(t)]) = 0 is discussed. The results obtained are extensions of some of the results by Kim (Proc. Amer. Math. Soc. 62 (1977), 77–82) for y(n) + py = 0

On the oscillation of solutions and existence of positive solutions of neutral difference equations

AbstractWe obtain sufficient conditions for the oscillation of all solutions and existence of positive solutions of the neutral difference equation Δ(xn + cxn − m) + pnxn − k = 0, n = 0, 1, 2, …, where c and pn are real numbers, m and k are integers, and pn, m and k are nonnegative

An Application of Discrete Inequality to Second Order Nonlinear Oscillation

AbstractBy using some simple discrete inequalities oscillation criteria are provided for the second order difference equations Δ2yn+an+1ƒ(yn+1)=0 n∈N where the operator Δ is defined by Δyn=yn+1−yn, {an} is a real sequence. The function ƒ is such that uƒ(u)>0 for u≠0 and ƒ(u)−ƒ(v)=g(u, v)(u−v) for u, v≠0 for some nonnegative function g

Discrete polynomial interpolation, Green's functions, maximum principles, error bounds and boundary value problems

Computers and Mathematics with Applications2583-39CMAP

On the oscillation of Volterra summation equations

summary:The asymptotic and oscillatory behavior of solutions of Volterra summation equations $$y_{n}=p_{n} \pm \sum _{s=0}^{n-1}K(n,s)f(s,y_{s}), \ n\in \mathbb{N}$$ where $\mathbb{N}=\lbrace 0,1,2,\dots \rbrace$, are studied. Examples are included to illustrate the results