【作者】 赵艳云；

【导师】 李成福；

【作者基本信息】 湘潭大学 ， 应用数学， 2007， 硕士

【摘要】 本文主要讨论了高阶非线性中立型偏差分方程正解的存在性问题和中立型椭圆偏差分方程的振动性问题。全文共分为三章。第一章，简要地介绍了前人对偏差分方程所取得的研究成果，并概括了本文的主要内容。第二章，基于已有的偏差分方程和差分方程的结果，我们研究了高阶非线性中立型偏差分方程多正解的存在性问题，建立了判断多正解存在的充分条件，对前人的结果进行推广。第三章，研究了中立型椭圆偏差分方程的边值问题的振动性，把中立型椭圆微分方程的两种边值问题的结果推广到中立型椭圆偏差分方程的边值问题中，得到了中立型椭圆偏差分方程的边值问题的解的振动性的充分必要条件。更多还原

【Abstract】 In this paper, we discuss the oscillation and nonoscillation of the solutions of the neutral partial difference equations. It is composed of three chapters.Chapter 1, we simply introduce some known results about partial difference equations and the main content of this paper.Chapter 2, we investigate the existence of multiple positive solutions of the neutral partial difference equations on the base of the existed results of partial difference and difference equations, and obtain some sufficient conditions for the existence of multiple positive solutions. This result extend some criteria obtained by the the forefather.Chapter 3, we consider the oscillation of the boundary problems of neutral parabolic partial difference equations. Some results for neutral functional parabolic equations are extend to neutral parabolic partial difference equations, some sufficient and necessary conditions under which every solution of the equations is oscillatory, are obtained.更多还原