Necessary and sufficient conditions for oscillation of first order nonlinear neutral 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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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2006
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2005.07.078