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

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

摘要/Abstract

摘要：

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.

关键词: oscillation, third order, mixed type neutral difference equation

Abstract:

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

中图分类号:

39A10

E. THANDAPANI, N. KAVITHA. OSCILLATORY BEHAVIOR OF SOLUTIONS OF CERTAIN THIRD ORDER MIXED NEUTRAL DIFFERENCE EQUATIONS[J]. 数学物理学报(英文版), 2013, 33(1): 218-226.

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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