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哈密顿系统的定性理论研究及应用
  • 项目名称：哈密顿系统的定性理论研究及应用
  • 项目类别：面上项目
  • 批准号：10771118
  • 申请代码：A010702
  • 项目来源：国家自然科学基金
  • 研究期限：2008-01-01-2010-12-31
  • 项目负责人：孟凡伟
  • 负责人职称：教授
  • 依托单位：曲阜师范大学
  • 批准年度：2007
中文摘要：

哈密顿系统的理论是现代数学中一个既有深刻理论又有广泛应用的研究领域，它来源于一切遵循哈密顿最小作用量原理的过程. 本项目研究哈密顿系统的一系列定性行为振动性及与对应的微分算子的本质谱下界之间的关系，离散谱的判别，Reid－Roundabout原理，GKN理论，极限点型(强极限点型)与极限圆型的判别，一维薛定谔方程的谱问题等。这些都是国内外这方面研究的前沿问题。其解决对最优控制、奇异摄动、计算力学、量子力学等多门学科有重要意义.

中文主题词： 哈密顿系统；定性理论；振动性；本质谱；离散谱。
结论摘要：

英文主题词Hamiltonian system;qualitative theory; oscillation;essential spectrum, discrete spectrum.

成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 61
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期刊论文
An Improved F-Expansion Method And Its Application to Coupled Drinfeld -Sokolov- Wilson Equation
Integral inequalities in two independent variables for retarded Volterra equations
Oscillation of second-order nonlinear ODE with damping
Extended Hyperbolic Function Rational Expansion Algorithm with Symbolic Computation to construct Sol
Hartman type oscillation criteria for linear matrix Hamiltonian systems
Oscillation criteria for second-order neutral equations with distributed deviating argument
Interval oscillation criteria for matrix differential systems with damping
一类时标动态方程的极限圆型判定准则及应用
两个Hamilton算子积的自伴性
偶阶半线性中立型分布时滞微分方程的振动性
ON SOME NEW RETARDED INTEGRAL INEQUALITIES AND THEIR APPLICATIONS
Positive solutions of the singular semipositone boundary value problem on time scales
Backward solutions to nonlinear integro-differential systems
Interval oscillation criteria for higher order neutral nonlinear differential equations with deviati
Oscillation theorems for second order forced nonlinear differential equations with delayed argument
OSCILLATION CRITERIA FOR MATRIX HAMILTONIAN SYSTEMS VIA THE SUMMABILITY METHOD
二阶具有偏差变元的积分微分方程解的渐近性(英文)
一类时标动态方程属于极限圆型的判定
Some generalized integral inequalities and their applications
On a class of Volterra nonlinear equations of parabolic type
Oscillation Theorems for Second-Order Forced Neutral Nonlinear Differential Equations with Delayed A
Oscillation Criteria for Even Order Neutral Equations with Distributed Deviating Argument
New Oscillation Criteria for Second-Order Delay Differential Equations with Mixed Nonlinearities
New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive and Neg
Limit behavior of the solution to nonlinear viscoelastic Marguerre von Karman shallow shells system
On Some Integral Inequalities on Time Scales and Their Applications
OSCILLATION CRITERIA FOR SECOND ORDER NEUTRAL PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS
一类新型具有两个独立变量的不连续函数的积分不等式
Uniform decay rates for nonlinear viscoelastic Marguerre-von Karman equations
Oscillation criteria for second order linear matrix differential systems with damping
Some new oscillation results for linear Hamiltonian systems
Oscillation of second-order delay differential equations with mixed nonlinearities
ON OSCILLATION PROPERTIES FOR LINEAR HAMILTONIAN SYSTEMS
一类 n 阶微分方程的振动性准则
OSCILLATION RESULTS RELATED TO INTEGRAL AVERAGING TECHNIQUE FOR LINEAR HAMILTONIAN SYSTEMS
New oscillation criteria for second-order nonlinear neutral delay differential equations
Oscillation criteria for forced second-order nonlinear differential equations with damping
Oscillation criteria for forced second order differential equations with mixed nonlinearities
Some new delay integral inequalities and their applications
Interval oscillation criteria for second order partial differential equations with delays
On certain integral inequalities in two independent variables for retarded equations
OSCILLATION CRITERIA FOR FORCED SUPERLINEAR DIFFERENCE EQUATIONS
OSCILLATION RESULTS RELATED TO INTEGRAL AVERAGING TECHNIQUE FOR EVEN ORDER NEUTRAL DIFFERENTIAL EQUATION WITH DEVIATING ARGUMENTS
ON SOME RETARDED INTEGRAL INEQUALITIES AND APPLICATIONS
OSCILLATION OF SOLUTIONS TO SECOND ORDER NEUTRAL PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS
OSCILLATION CRITERIA FOR SECOND ORDER QUASILINEAR NEUTRAL EQUATION
新的双曲函数有理展开法和符号计算构造差分mKdV的孤波解(英文)
一类具有时滞的中立型双曲微分方程解的振动性
具有收获率和Michaelis-Menten功能性反应的捕食系统的稳定性和Hopf分支
一类二阶非线性具有偏差变元的微分方程解的有界性
一些广义的积分不等式及其应用
带阻尼项的二阶拟线性非齐次微分方程的振动性判据
一类线性二阶自共轭矩阵微分系统的两点振动性研究
会议论文
Oscillation Theorems for High-Order Neutral Nonlinear Differential Equations
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