【作者】 肖娟；

【导师】 罗治国；

【作者基本信息】 湖南师范大学 ， 基础数学， 2005， 硕士

【摘要】 本硕士论文由三章组成。 第一章,研究具非线性中立项时滞差分方程方程 Δ(x_n-px_n-τ^α)+q_nx_n-σ^β=0,n≥n₀正解的存在性。 第二章,首先获得了具非线性中立项时滞差分方程 Δ(x_n-px_n-τ^α)+q_nx_n-σ^β=0,n≥n₀在以下两种情形 （ⅰ）.α∈（1,∞）,β∈（0,∞）;（ⅱ）.α=1,β∈（0,∞）下有界解振动的几个充要条件,接着进一步研究了在条件α>1,0<β≤α下上述方程解的振动性和非振动性,获得了几乎“sharp”振动和非振动准则。 第三章,我们证明了奇数阶中立型差分方程 Δ^m(x_n-px_n-τ^α)+q_nx_n-σ^β=0,n≥n₀在条件（α-1）²+（p-1）²>0和sum from s=n₀ to ∞ s^m-1q_s<∞下正解的存在性。 我们获得的结论改进和推广了相应文献中的结果,并且所获得的几乎“sharp”振动和非振动准则是第一次给出,填补了已有文献中的空白。文中的例子说明了我们结果的有效性。更多还原

【Abstract】 The thesis of Master’s Degree is composed of three chapters. In the first chapter, We study the existence of positive solutions for delay difference equations with a nonlinear neutral termIn chapter two, the oscillatory behavior of solutions of delay difference equations with nonlinear neutral termis studied firstly in the case. Next tow almost " sharp " oscillatory and nonoscillatory criteria are obtained.In chapter three ,we study the existence of positive solutions for the odd-order delay difference equations with a nonlinear netural termunder the conditions that (a — l)~2 + (p— 1)~2 > 0 and .which generalize the exist results in the literature.Our results improve and extend the all known results in related literature .Moreover the theorems of almost " sharp " oscillatory and nonoscillatory criteria are firstly obtained ,which filla gap in the literature.Some examples given in the paper illutrate the effect of our results.更多还原