Survey of Oscillation Criteria for First Order Delay Differential Equations
نویسنده
چکیده
In this paper, we discuss the oscillatory behavior of first order delay differential equations of the form: y′(t) + p(t)y(τ(t)) = 0, t ≥ T, where p and T are continuous functions defined on [T,∞), p(t) > 0, τ(t) < t for t ≥ T, τ(t) is nondecreasing and lim t→∞ τ(t) = ∞. We present best possible conditions for the oscillation of all solutions for this equation.
منابع مشابه
Some Oscillation Criteria For First Order Delay Dynamic Equations
We present an oscillation criterion for first order delay dynamic equations on time scales, which contains well-known criteria for delay differential equations and delay difference equations as special cases. We illustrate our results by applying them to various kinds of time scales.
متن کاملNew oscillation criteria for first order nonlinear neutral delay differential equations
Oscillation criteria are obtained for all solutions of first-order nonlinear neutral delay differential equations. Our results extend and improve some results well known in the literature. Some examples are considered to illustrate our main results.
متن کاملOscillation of third order trinomial delay differential equations
The purpose of this paper is to study oscillation and asymptotic behavior of solutions to a third order linear delay differential equation . All righ in part t Umeå Baculíko y000ðtÞ þ pðtÞy0ðtÞ þ qðtÞyðsðtÞÞ 1⁄4 0: New comparison theorems deduce oscillation of the given third order delay differential equation via application of known oscillation criteria to associated first order delay differen...
متن کاملA Parameter Uniform Numerical Scheme for Singularly Perturbed Differential-difference Equations with Mixed Shifts
In this paper, we consider a second-order singularly perturbed differential-difference equations with mixed delay and advance parameters. At first, we approximate the model problem by an upwind finite difference scheme on a Shishkin mesh. We know that the upwind scheme is stable and its solution is oscillation free, but it gives lower order of accuracy. So, to increase the convergence, we propo...
متن کاملNonlinear oscillation of certain third-order neutral differential equation with distributed delay
The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...
متن کامل