几类二阶离散Hamilton系统的同宿轨
发布时间：2018-11-08 11:24
【摘要】：本文主要应用变分法研究了几类二阶离散Hamilton系统同宿轨的存在性和多重性,在现有结果的基础上减弱非线性项的控制条件后得到相应的结论,推广和改进了已有的工作.我们通过构造变分结构与工作空间,寻求系统所对应泛函的近似临界点序列,进而证明系统解的存在性与多重性.全文大致可以分为三个部分,分别为：第一部分：介绍了问题产生的背景、研究现状以及临界点理论中的一些比较重要的基本知识.第二部分：研究超二次二阶离散Hamilton系统在L(t)不是全局正定,b(t)变号,并且V(u(t))关于u是超二次的情况下,应用临界点理论中的山路定理得到了系统同宿轨的存在性与多重性.第三部分：研究次二次二阶离散Hamilton系统是次二次的情况下,利用极小作用原理,在新的假设和新的条件下应用临界点理论得到了同宿轨的存在性.
[Abstract]:In this paper, the existence and multiplicity of homoclinic orbits for several second order discrete Hamilton systems are studied by using variational method. Based on the existing results, the control conditions of nonlinear terms are weakened and the corresponding conclusions are obtained, which generalize and improve the existing work. By constructing the variational structure and workspace, we seek the approximate critical point sequence of the functional corresponding to the system, and prove the existence and multiplicity of the solution of the system. The whole paper can be divided into three parts: the first part introduces the background of the problem, the present situation of the research and some important basic knowledge in the critical point theory. In the second part, we study the super-quadratic discrete Hamilton system under the condition that L (t) is not a global positive definite, b (t) sign and V (u (t) is super quadratic. The existence and multiplicity of homoclinic orbits are obtained by using the mountain path theorem in the critical point theory. In the third part, we study the existence of homoclinic orbits under new assumptions and new conditions by applying the critical point theory to the case that the second order discrete Hamilton system is of the second quadratic order, using the minimal action principle.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175
，
本文编号：2318348
[Abstract]:In this paper, the existence and multiplicity of homoclinic orbits for several second order discrete Hamilton systems are studied by using variational method. Based on the existing results, the control conditions of nonlinear terms are weakened and the corresponding conclusions are obtained, which generalize and improve the existing work. By constructing the variational structure and workspace, we seek the approximate critical point sequence of the functional corresponding to the system, and prove the existence and multiplicity of the solution of the system. The whole paper can be divided into three parts: the first part introduces the background of the problem, the present situation of the research and some important basic knowledge in the critical point theory. In the second part, we study the super-quadratic discrete Hamilton system under the condition that L (t) is not a global positive definite, b (t) sign and V (u (t) is super quadratic. The existence and multiplicity of homoclinic orbits are obtained by using the mountain path theorem in the critical point theory. In the third part, we study the existence of homoclinic orbits under new assumptions and new conditions by applying the critical point theory to the case that the second order discrete Hamilton system is of the second quadratic order, using the minimal action principle.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175
，
本文编号：2318348
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