一类基尔霍夫问题和一类哈密顿系统问题解的存在性
发布时间：2018-11-04 12:10
【摘要】：变分法是研究泛函极值的门数学分支.它的起源可以是最早追溯到约翰.伯努利的最速下降问题.古典的变分理论是将微分方程求解问题转化成确定相应泛函的极大极小问题,已经成为研究方程边值问题的基本方法.二十世纪,变分法有了新的进展,如山路定理,喷泉定理,环绕定理.本文通过变分法来得到基尔霍夫方程和哈密顿系统问题解的存在性.根据研究内容分为以下三章：第一章概述了一些本专业的基本知识及相关的理论渊源.第二章研究一类基尔霍夫问题其中Ω(?)R3的光滑有界区域,我们将得出上述问题存在基态变号解：第三章研究一类二阶哈密顿顿系统其中W(t,u)是超二次的.我们通过局部环绕定理和形变引理,将得到至少两个非平凡同宿轨道.
[Abstract]:Variational method is a branch of gate mathematics for studying functional extremum. Its origins can be traced back to John. Bernoulli's fastest drop problem. The classical variational theory is to transform the solving problem of differential equation into a minimax problem to determine the corresponding functional. It has become the basic method to study the boundary value problem of equation. In the twentieth century, the variational method has made new progress, such as mountain path theorem, fountain theorem, surround theorem. In this paper, the existence of solutions for Kirchhoff equation and Hamiltonian system problem is obtained by variational method. There are three chapters according to the research content: the first chapter summarizes some basic knowledge and related theoretical sources. In the second chapter, we study a class of Kirchhoff problem, where 惟 (?) R3 is a smooth bounded region, and we obtain the existence of a ground state sign change solution for the above problem. In Chapter 3, we study a class of second-order Hamiltonian systems in which W (Tu) is superquadratic. We obtain at least two nontrivial homoclinic orbits by means of local surround theorem and deformation Lemma.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175
本文编号：2309776
[Abstract]:Variational method is a branch of gate mathematics for studying functional extremum. Its origins can be traced back to John. Bernoulli's fastest drop problem. The classical variational theory is to transform the solving problem of differential equation into a minimax problem to determine the corresponding functional. It has become the basic method to study the boundary value problem of equation. In the twentieth century, the variational method has made new progress, such as mountain path theorem, fountain theorem, surround theorem. In this paper, the existence of solutions for Kirchhoff equation and Hamiltonian system problem is obtained by variational method. There are three chapters according to the research content: the first chapter summarizes some basic knowledge and related theoretical sources. In the second chapter, we study a class of Kirchhoff problem, where 惟 (?) R3 is a smooth bounded region, and we obtain the existence of a ground state sign change solution for the above problem. In Chapter 3, we study a class of second-order Hamiltonian systems in which W (Tu) is superquadratic. We obtain at least two nontrivial homoclinic orbits by means of local surround theorem and deformation Lemma.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175
【参考文献】
相关期刊论文 前1条
1 ;PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEA RHAMILTONIAN SYSTEMS[J];Chinese Annals of Mathematics;1997年03期
，本文编号：2309776
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