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跨共振点非耗散振动周期解存在性研究
  • 项目名称：跨共振点非耗散振动周期解存在性研究
  • 项目类别：面上项目
  • 批准号：10771212
  • 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：刘文斌
  • 负责人职称：教授
  • 依托单位：中国矿业大学
  • 批准年度：2007
中文摘要：

本项目研究跨共振点非耗散振动方程周期解存在性和高阶、高维微分方程Fucik谱的结构。通过分析振动势能和振动刚性系数间的关系，和利用振动的共振点控制振动势能的变化，得到跨共振点情况下，非耗散振动方程周期解存在的若干充分条件；并对所研究的振动系统进行数值分析，为工程技术、经济分析等相关问题提供理论支撑。在广义Fucik谱框架下，对频率不对称的时变强迫振动方程周期解存在性给出更精确估计，对高阶和高维振动方程周期解存在性提供一个更有效的判据；所得结果将改进、丰富已有工作。

中文主题词： 共振点；非耗散；非线性振动；周期解；Fucik谱
成果综合统计
成果类型
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  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 74
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期刊论文
Uniqueness and existence results for a third-order nonlinear multi-point boundary value problem
Existence of large solution of a class of quasilinear elliptic equations with singular boundary
The existence of large solutions of semilinear elliptic equations with negative exponents
Positive solutions for nonlinear semipositione nth-order boundary value problems
Existence of positive solutions for fourth-order three-point boundary value problems
Triple positive solutions for second-order four-point boundary value problem with sign changing nonl
Positive solutions to a singular n-th order three-point boundary value problem with sign changing no
Antiperiodic boundary value problems for second-order impulsive ordinary differential equations
Existence of solutions for fourth-order four-point boundary value problem on time scales
Existence of positive solutions for a functional fractional boundary value problem
Existence of anti-periodic solutions for third order differential systems
Positive solutions for second-order four-point boundary value problems with alternating coefficient
Global stability of almost periodic solutions of Hopfield neural networks with neutral time-varying
Anti-periodic solutions for higher-order nonlinear ordinary differential equations
The multiple positive solutions for p-Laplacian multipoint BVP with changing nonlinearity on time sc
Existence of multiple positive solutions for nth-order p-Laplacian m-point singular boundary value p
A system of nonlinear system of nonlinear set-valued implicit variational inclusions in real Banach
Problems of periodic solutions for a type of Duffing equation with state-dependent delay
Triple positive solutions of three-point boundary value problems for fourth-order differential equat
Triple positive solutions for a boundary value problem of nonlinear fractional differential equation
Positive solutions for second-order three-point eigenvalue problems
一阶非线性脉冲微分方程边值问题解的存在性
四阶p-Laplacian中立型泛函微分方程周期解的存在性
Green's function and positive solutions of a singular nth-order three-point boundary value problem o
Existence of positive solutions for boundary value problems of fractional functional differential eq
一类高阶中立型微分方程周期解的存在性
一类具多偏差变元的p-Laplacian方程周期解的存在性
角函数方法在二阶微分方程边值问题中的应用
非线性四阶周期边值问题多个正解的存在性
一类三阶微分方程边值问题的单调迭代法
一类三阶两点边值单调正解的存在性与多解性
非连续三点边值问题在非共振条件下的弱解
n阶非线性两点奇异边值问题单调正解的存在性
具有时滞的Rayleigh方程周期解的存在性与唯一性
Periodic solutions for p-Laplacian systems of Lienard-type
Existence of solutions to three-point boundary value problem for one-dimensional p-Laplacian
A nonlinear third order multi-point boundary value problem in the resonance case
Generalized Ekeland's variational principle on generalized metric space
Unbounded upper and lower solutions method for third-order boundary-value problems on the half-line
Solvability of multi-point value problem
The existence and multiplicity of solutions to p-Laplace equation with periodic boundary conditions
Singular perturbation of a second-order three-point boundary value problem for nonlinear systems
Impulsive boundary-value problems for first-order integro-differential equations
一类带有变号二阶四点奇异边值问题的正解
一类p-Laplacian方程边值问题解的存在性
二阶积分-微分方程周期边值问题正解的存在性
时滞Hopfield神经网络的稳定性研究
Existence of multiple positive solutions of higher order multi-point nonhomogeneous boundary value p
Existence and stability of almost periodic solutions of Hopfield neural networks with continuously d
Existence of periodic solutions for p-Laplacian equation under the frame of Fucik spectrum
Anti-symmetric periodic solutions for the third order differential systems
Antiperiodic solutions for Lienard-type differential equation with p-Laplacian operator
Multiple periodic solutions of p-Laplacian equation with one-side Nagumo condition
A second order multivalued boundary value problem and impulsive neutral functional differential incl
Existence of solutions for three-point boundary value problem at resonance
New result of existence of periodic solution for a Hopfield neural networks with neutral time-varyin
非线性三阶三点边值问题的正解
Fixed Point Theorems in Cone Symmetric Spaces
一类分数阶微分方程三点边值问题正解的存在性
分数微分方程边值问题正解的存在与不存在性
非线性分数阶微分方程边值问题解的唯一性
Common Fixed Points under Contractive Conditions in Cone Metric Spaces
偏距离空间上四个映射的公共不动点的存在性与唯一性
一类四阶边值问题的正解的存在性与多重性
POSITIVE SOLUTIONS TO A SINGULAR nTH ORDER THREE-POINT BOUNDARY VALUE PROBLEM WITH SIGN CHANGING NONLINEARITY
共振条件下分数阶微分方程多点边值问题解的存在性
带有p-Laplacian的二阶三点微积分边值问题伪对称正解的存在性
一类非线性四阶微分方程三点边值问题的可解性
时标上具有m点边值条件的二阶动力包含解的存在性
Banach空间中分数阶微分方程初值问题解的性质
一类共振条件下分数阶多点边值问题的可解性
二阶积分-微分方程周期边值问题解的存在性
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刘文斌的项目
保守振动方程周期解的存在性研究
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