二阶耦合差分系统边值问题

发布时间：2018-06-27 13:33

本文选题：耦合系统 + 差分方程　；参考：《广州大学》2017年硕士论文

【摘要】：本文主要研究了二阶耦合差分系统边值问题非平凡解的不存在性和存在性.首先,我们建立适当的变分泛函,将寻求耦合差分系统边值问题非平凡解的存在性转化为对应泛函的临界点的存在性.在系数满足一定条件下,我们研究了耦合差分系统边值问题非平凡解的不存在性,然后应用临界点定理,得到了相应耦合差分系统边值问题存在非平凡解的一系列充分条件.全文的结构如下:第一章简述了问题产生的历史背景和研究意义,相关的预备知识以及已有结果和本文的主要工作.第二章在系数满足一定条件下,研究了二阶耦合差分系统边值问题非平凡解的不存在性.第三章利用临界点定理,研究了二阶耦合差分系统边值问题非平凡解的存在性.
[Abstract]:In this paper, the nonexistence and existence of nontrivial solutions of boundary value problems for second order coupled difference systems are studied. First of all, we establish appropriate variational functional and transform the existence of nontrivial solution to the critical point of the corresponding functional from seeking the existence of nontrivial solution for the boundary value problem of coupled difference system to the existence of the critical point of the corresponding functional. In this paper, we study the nonexistence of nontrivial solutions for boundary value problems of coupled difference systems under certain conditions. Then, by applying the critical point theorem, we obtain a series of sufficient conditions for the existence of nontrivial solutions for boundary value problems of coupled difference systems. The structure of the thesis is as follows: in Chapter 1, the historical background and research significance of the problem are briefly introduced, the relevant preparatory knowledge, the existing results and the main work of this paper are also discussed. In chapter 2, we study the nonexistence of nontrivial solutions for boundary value problems of second order coupled difference systems under certain conditions. In chapter 3, by using the critical point theorem, we study the existence of nontrivial solutions for boundary value problems of second order coupled difference systems.
【学位授予单位】：广州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.7

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