Necessary and Sufficient Conditions of Oscillation in First Order Neutral Delay Differential Equations
نویسندگان
چکیده
منابع مشابه
Necessary and sufficient conditions for oscillation of first order neutral delay difference equations
In this paper, we obtained some necessary and sufficient conditions for oscillation of all the solutions of the first order neutral delay difference equation with constant coefficients of the form ∆[x(n)− px(n− τ)] + qx(n− σ) = 0, n ≥ n0 (∗) by constructing several suitable auxiliary functions. Some examples are also given to illustrate our results.
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In this paper, we establish the necessary and sufficient conditions for oscillation of the following first order neutral delay difference equation ∆[x(n) + px(n− τ)] + qx(n− σ) = 0, n ≥ n0, (∗) where τ and σ are positive integers, p 6= 0 is a real number and q is a positive real number. We proved that every solution of (∗) oscillates if and only if its characteristic equation (λ− 1)(1 + pλ−τ ) ...
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We establish some new criteria for the oscillation of second-order Emden–Fowler neutral delay differential equations.We study the case of superlinear and the case of sublinear equations subject to various conditions. The results obtained show that the presence of a neutral term in a differential equation can cause or destroy oscillatory properties. Several examples are provided to illustrate th...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2014
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2014/623713