OSCILLATORY BEHAVIOR OF SOLUTIONS OF CERTAIN THIRD ORDER MIXED NEUTRAL DIFFERENCE EQUATIONS

doi:10.1016/S0252-9602(12)60206-9

Abstract

Abstract:

The objective of this paper is to study the oscillatory and asymptotic prop-erties of the mixed type third order neutral difference equation of the form
Δ(a_nΔ² (x_n + b_nx_n_−τ1 + c_nx_n_+τ2 ))+ q_nx^β_n_+1−σ1 p_nx^β_n_+1+σ2= 0,
where {a_n} , {b_n} , {c_n} , {q_n} and {p_n} are positive real sequences, β is a ratio of odd positive integers, τ₁, τ₂, σ₁ and σ₂ are positive integers. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converges to zero. Some examples are presented to illustrate the main results.

Key words: oscillation, third order, mixed type neutral difference equation

CLC Number:

39A10

E. THANDAPANI, N. KAVITHA. OSCILLATORY BEHAVIOR OF SOLUTIONS OF CERTAIN THIRD ORDER MIXED NEUTRAL DIFFERENCE EQUATIONS[J].Acta mathematica scientia,Series B, 2013, 33(1): 218-226.

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