一类多滞量的非线性偏差分方程的渐近稳定性

【作者】 侯成敏；

【导师】 崔成日；

【作者基本信息】 延边大学 ， 基础数学， 2007， 硕士

【摘要】 偏差分方程是含有两个或两个以上独立变量的差分方程，在用有限差分法求偏微分方程近似解中，在研究分子轨道、数学物理方程等问题中常常会遇到这类方程，本文主要研究一类多滞量的非线性偏差分方程。全文共分三章。第一章，主要对所研究的问题的背景、研究现状及本文所做的工作作了概括性的描述。第二章，给出了本文所涉及的基本概念及引理，为了正文的需要在引理2中构造了一个收敛序列，并给出了相应的证明。第三章是本文的主要内容。首先研究了方程解的振动性和持久性，建立了振动性和持久性的充分条件。其次，将方程的解与引理2中所构造的收敛序列进行比较，利用数学归纳法证明了解的一致稳定性，最后，利用上下确界的性质证明了解的吸引性，从而获得偏差分方程解的一致渐近稳定性结果。更多还原

【Abstract】 The partial difference equations (PDES)are difference equation thatinvolve functions of two or more independent variables. Such equations occur frequentlyin finding the approximate solutions of partial differential equations by finite differencemethods, and in studying on molecular orbits and mathematical physics equationsetc.This paper are divided into three chapters.In chapter 1 the historical background, present searching situation of the researchproblem and the major research work of this paper are described.In chapter 2 basic definitions and lemma this paper involves are introduced. Inorder to prove our main theorem, a convergent sequence are established in lemma 2and the corresponding proof is made.In chapter 3 the main content of this paper are contained. First, the oscillationand permanence of the solutions of partial differential equations are studied and thecorresponding sufficient conditions are established. Next, the solutions of partial difference equations and the convergent sequences in lemma 2 are compared. By means ofmathematical induction method, uniform stability of the solutions of partial differentialequations are obtained. Finally, the attraction of the the solutions of partial differenceequations is prove by using properties of supremum and infimum, thus the uniformasymptotic stability of the solutions of partial difference equation are obtained.更多还原