Existence of Oscillatory and Nonoscillatory Solutions for a Class of Neutral Functional Differential Equations
نویسنده
چکیده
For a certain class of functional dierential equations with perturbations conditions are given such that there exist solutions which converge to solutions of the equations without perturbation. Let ∆ x(t) = x(t) − x(t − σ), σ > 0 being a constant, and consider the neutral functional diierential equation (A) d n dt n ∆ m x(t) + f ? t, x ? g(t) is the m-th iterate of ∆ , i.e. ∆ m x(t) = m X i=0 (−1) i m i x(t − iσ).
منابع مشابه
Existence of Oscillatory Solutions for Functional Differential Equations of Neutral Type
One of the important problems in the qualitative theory of functional differential equations of neutral type, which has currently received wide attention, is to discuss the existence of solutions, either oscillatory or nonoscillatory, of the equation under consideration. As far as the nonoscillatory solutions are concerned, there has been a lot of systematic investigations, and numerous results...
متن کاملExistence and continuous dependence for fractional neutral functional differential equations
In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.
متن کاملExistence of Nonoscillatory and Oscillatory Solutions of Neutral Differential Equations with Positive and Negative Coefficients
In this paper, we study the existence of oscillatory and nonoscillatory solutions of neutral differential equations of the form ( x(t)− cx(t− r))′ ± (P (t)x(t− θ)−Q(t)x(t− δ)) = 0 where c > 0, r > 0, θ > δ 0 are constants, and P , Q ∈ C( +, +). We obtain some sufficient and some necessary conditions for the existence of bounded and unbounded positive solutions, as well as some sufficient condit...
متن کاملOscillation and Nonoscillation Theorems for a Class of Even-order Quasilinear Functional Differential Equations
We are concerned with the oscillatory and nonoscillatory behavior of solutions of evenorder quasilinear functional differential equations of the type (|y(n)(t)|α sgn y(n)(t))(n) + q(t)|y(g(t))|β sgn y(g(t))= 0, where α and β are positive constants, g(t) and q(t) are positive continuous functions on [0,∞), and g(t) is a continuously differentiable function such that g′(t) > 0, limt→∞ g(t)=∞. We ...
متن کاملClassification of Nonoscillatory Solutions of Nonlinear Neutral Differential Equations
Nonoscillatory solutions of a general class of second order functional neutral differential equations of the form
متن کامل