Oscillation and nonoscillation in nonlinear third order difference equations
نویسندگان
چکیده
منابع مشابه
Oscillation 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.
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(ii) {g(n)} is a nondecreasing sequence, and limn→∞ g(n)=∞; (iii) f ∈ (R,R), x f (x) > 0, and f ′(x)≥ 0 for x = 0; (iv) αi, i= 1,2, are quotients of positive odd integers. The domain (L3) of L3 is defined to be the set of all sequences {x(n)}, n ≥ n0 ≥ 0 such that {Ljx(n)}, 0≤ j ≤ 3 exist for n≥ n0. A nontrivial solution {x(n)} of (1.1;δ) is called nonoscillatory if it is either eventually posi...
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In this paper some new sufficient conditions for the oscillation of solutions of the third order half-linear difference equations ∆ ( an(∆ (xn + bnh(xn−δ))) α ) + qnf(xn+1−τ ) = 0 and ∆ ( an(∆ (xn − bnh(xn−δ))) α ) + qnf(xn+1−τ ) = 0 are established. Some examples are presented to illustrate the main results.
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1990
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171290000412