Oscillation, Nonoscillation and Growth of Solutions of Generalized Nonlinear Difference Equation of Second Order

Oscillation and Non oscillation of Solutions of Generalized Nonlinear Difference Equation of Second Order

“…In [3] the author considered = 1 and k ∈ N(a) for an integer a but, in this paper the theory is extended for all real k ∈ [a, ∞) and for any real and oscillation and nonoscillation of solutions of the generalized nonlinear difference equation (1) is discussed. The results of this paper generalize those of ( [4,5,11]). Throughout this paper, we use the following notations.…”

“…Suppose that conditions (c 1 ), (c 6 ) and (c 8 ) hold and for every constants C 1 , C 2 > 0, a + j + r ) + C 1 f (a + j + r )) + C 2 R a+j,k < 0 (11). …”

Oscillatory and Nonoscillatory Behaviour of Solutions of Generalized Mixed Difference Equations

“…Definition 2.4. [11] The solution u(k) of a generalized difference equation is called oscillatory if for any…”

GLOBAL PROPERTIES OF SOLUTIONS OF FOURTH ORDER GENERALIZED alpha-DIFFERENCE EQUATIONS

“…Definition 2.1. [8] Let u(k), k ∈ [0, ∞) be a real or complex valued function and ℓ ∈ (0, ∞). Then, the generalized α-difference operator ∆ α(ℓ) on u(k) is defined as in (3).…”