【摘要】：變分法是研究泛函極值的門數(shù)學(xué)分支.它的起源可以是最早追溯到約翰.伯努利的最速下降問(wèn)題.古典的變分理論是將微分方程求解問(wèn)題轉(zhuǎn)化成確定相應(yīng)泛函的極大極小問(wèn)題,已經(jīng)成為研究方程邊值問(wèn)題的基本方法.二十世紀(jì),變分法有了新的進(jìn)展,如山路定理,噴泉定理,環(huán)繞定理.本文通過(guò)變分法來(lái)得到基爾霍夫方程和哈密頓系統(tǒng)問(wèn)題解的存在性.根據(jù)研究?jī)?nèi)容分為以下三章：第一章概述了一些本專業(yè)的基本知識(shí)及相關(guān)的理論淵源.第二章研究一類基爾霍夫問(wèn)題其中Ω(?)R3的光滑有界區(qū)域,我們將得出上述問(wèn)題存在基態(tài)變號(hào)解：第三章研究一類二階哈密頓頓系統(tǒng)其中W(t,u)是超二次的.我們通過(guò)局部環(huán)繞定理和形變引理,將得到至少兩個(gè)非平凡同宿軌道.
[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.
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 ;PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEA RHAMILTONIAN SYSTEMS[J];Chinese Annals of Mathematics;1997年03期

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本文編號(hào)：2309776