Necessary and sufficient conditions for oscillation of first-order nonlinear neutral difference 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.
متن کاملNecessary and sufficient conditions for oscillations of first order neutral delay difference equations with constant coefficients
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 ) ...
متن کاملNecessary and Sufficient Condition for Oscillation of Higher Order Nonlinear Delay Difference Equations
-This paper is concerned with the oscillation of solutions of higher order nonlinear delay difference equations with forcing terms of the form Anx(t) + f(t, x(t),x(a(t))) = h(t), t E I = {0, 1 . . . . }, where A is the forward difference operator defined by Ax(t) = x(t + 1) -x(t) and A'nx(t) = A(Am-lx(t)), m > 1. A necessary and sufficient condition is established under which every solution x(t...
متن کاملOscillation of second order nonlinear neutral delay difference equations
In this paper sufficient conditions are obtained for oscillation of all solutions of a class of nonlinear neutral delay difference equations of the form ∆(y(n) + p(n)y(n−m)) + q(n)G(y(n − k)) = 0 under various ranges of p(n). The nonlinear function G,G ∈ C(R,R) is either sublinear or superlinear. Mathematics Subject classification (2000): 39 A 10, 39 A 12
متن کاملOscillation Criteria of Third Order Nonlinear Neutral Difference Equations
In this paper we consider the third order nonlinear neutral difference equation of the form ∆(rn(∆(xn ± pnxσ(n)))) + f (n, xτ(n)) = 0, we establish some sufficient conditions which ensure that every solution of this equation are either oscillatory or converges to zero. Examples are provided to illustrate the main results.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2008
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2007.06.009