【作者】 贾茗；

【导师】 申建华；

【作者基本信息】 湖南师范大学 ， 基础数学， 2006， 硕士

【摘要】 本硕士论文由四章组成,主要讨论一类带阻尼项的高阶非线性中立型差分方程的正解的存在性,一类差分方程解的振动准则,一类非自治变时滞Logistic方程的全局吸引性,一类带有多个时滞微分方程的周期解。 第一章讨论了一类带阻尼项的高阶非线性中立型差分方程正解的存在性,利用Krasnoselskii不动点定理,得到了非振动解存在的若干充分必要条件,这些结果改进和推广了一些已知的结果. 第二章讨论了一类带两个时滞的差分方程解的振动性,给出了所有解振动的新的充分条件,并将其推广,得到了更一般的具有多时滞的差分方程解的振动性的准则,我们的结果推广了已有文献的结果. 第三章讨论了一类可变时滞非自治Logistic方程的正稳态是全局吸引子的充分条件,所得到的结果推广和改进了相关文献中的结果. 第四章利用重合度理论讨论了一类具有多个时滞的微分方程的周期解的存在性。更多还原

【Abstract】 This thesis of Master is composed of four chapters, which mainly studied the existence of non-oscillatory solutions of a class of higher-order nonlinear neutral difference equations with a forced term, oscillation criteria for a class of difference equations ,global attractivity for a class of nonautonomous variable delay-logistic equation,and existence of periodic solutions for differential equation with several delays.In chapter one, by using Krasnoselskii’s fixed point theorem, necessary and sufficient conditions of the existence of non-oscillatory solutions of a class of higher-order nonlinear neutral difference equation with a forced term are obtained. Our results extend the results of the some known results.Chapter two , sufficient conditions of oscillation of all solutions for the first order delay difference equation with two delays are obtained , and we use the criteria to the difference equation with several delays. Our results extend the known results of many authors.Chapter three, sufficient conditions are obtained for the positive steady state of the nonautonomous variable delay-Logistic equation to be a global attractor, which extend and improve the results in the known literature.In the last chapter, by using coincide degree theory ,the existences of periodic solution for a kind of differential equation with several delays are obtained.更多还原