【摘要】：本文主要研究線性與非線性Hamilton系統(tǒng)中的一些問題.全文分成兩部分.第一部分討論凸線性Hamilton系統(tǒng)基本解矩陣地R(t)在單位圓周上的特征值的變化規(guī)律.假設A(t)(t≥ 0)為連續(xù)對稱正定的2n階矩陣,J為標準辛矩陣,(?)(t) = JA(t)R(t), R(0) = I2n.假設λ∈σ(R(t0))∩U,其中t 0, U為單位圓周,定義mt為R(t)在λ附近并且在U上的特征值個數(shù),我們將用數(shù)值計算方法驗證猜測:當t→t0±時,mt是常數(shù).第二部分討論二階Hamilton系統(tǒng)(?)+ V'(t,x) = 0,x(1) - x(0) = 0,(?)(1) - (?)(0) = M1的解的存在性問題,其中V ∈C1([0,1] × Rn,R).利用拓撲同倫延拓方法將我們要討論的問題轉(zhuǎn)化為(?)+ (1-λ)B(t)x(t) + λV'(t, x) = 0,t∈[0,1],(?)(1) - (?)(0) = 0,x(1) - x(0) = AM1來進行分析,其中M1(x(0),(?)(0),x(1),(?)(1))簡寫為M1 , λ∈(0,1).從而給出了一個非零解的存在性證明.
[Abstract]:In this paper, some problems in linear and nonlinear Hamilton systems are studied. The full text is divided into two parts. In the first part, we discuss the change rule of the eigenvalues of the basic solution moment position R (t) of the convex linear Hamilton system on the unit circumference. Let A (t) (t 鈮，

本文編號：2467583