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测度链上时滞动力方程的周期解和边值问题
  • 项目名称：测度链上时滞动力方程的周期解和边值问题
  • 项目类别：面上项目
  • 批准号：10571078
  • 申请代码：A010701
  • 项目来源：国家自然科学基金
  • 研究期限：2006-01-01-2008-12-31
  • 项目负责人：李万同
  • 负责人职称：教授
  • 依托单位：兰州大学
  • 批准年度：2005
中文摘要：

本项目首先利用拓扑度理论和不动点理论，通过引入刻画非线性项在零和无穷处性态指标的框架下，研究了测度链上p-Laplacian动力方程的边值问题正解的存在性、多重性和性态及其特征值问题，并借助于上下解方法探讨了变号非线性项对解的定性性质的影响。其次，建立了周期动力方程的解的有界性和周期解存在性的联系，即Massera定理，并利用分支理论探讨了时滞引起的周期现象。第三，通过Rynne最近定义的积分，给出了临界点理论在研究非周期动力方程周期解存在的方法，由此研究了测度链上一类二阶Hamiltonian系统并得到了周期解的存在准则。也就是说，建立了测度链分析理论的变分方法。最后，建立了非局部时滞扩散系统的行波解和整体解的存在性和稳定性理论，并发现时间时滞降低最小传播速度而空间非局部作用加快最小传播速度的新现象。

中文主题词： 测度链；动力方程；非线性分析；周期解；边值问题；非局部时滞；扩散系统
结论摘要：

英文主题词time scales；dynamic equation；nonlinear analysis； periodic solution； boundary value problem；nonlocal delay；diffusive system

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期刊论文
Triple positive pseudo-symmetric solutions of three-point BVPs for p-Laplacian dynamic equations on
Bistable wavefronts in a diffusive and competitive Lotka-Volterra type system with nonlocal delays
Positive solutions of singular p-Laplacian dynamic equations with sign changing nonlinearity
Entire solutions in monostable reaction-diffusion equations with delayed nonlinearity
On the number of positive solutions of systems of nonlinear dynamic equations on time scales
Triple positive solutions of m-point BVPs for p-Laplacian dynamic equations on time scales
Stability and Hopf bifurcation for a delayed cooperative system with diffusion effects
Entire solutions in reaction-advection-diffusion equations in cylinders
测度链上p-Laplacian边值问题的三个正对称解
Positive solutions of p-Laplacian m-point boundary value problems on time scales
Traveling fronts in monostable equations with nonlocal delayed effects
Stability and Hopf bifurcation for a delayed cooperation diffusion system with Dirichlet boundary co
Positive solutions of singular p-Laplacian BVPs with sign changing nonlinearity on time scales
Multiple positive solutions for p-Laplacian m-point boundary value problems on time scales
测度链上非线性m-点边值问题的正解
偶数阶Sturm-Liouville边值问题的多个正解
Travelling wave fronts in reaction-diffusion systems with spatio-temporal delays
Existence of travelling wave solutions in delayed reaction–diffusion systems with applications to di
Stability and bifurcation in a simplified four-neuron BAM neural network with multiple delays
Hopf bifurcation and global periodic solutions in a delayed predator–prey system
Dynamics of a nonautonomous semiratio-dependent predator-prey system with nonmonotonic functional re
Eigenvalue problems for second-order nonlinear dynamic equations on time scales
Positive solutions of the nonlinear fourth-order beam equation with three parameters (II)
Periodic solution for non-autonomous second order Hamiltonian systems on time scales
一类非线性项变号的奇异p-Laplacian动力方程正解的存在性
Bifurcation and global periodic solutions in a delayed facultative mutualism system
Existence theory for positive solutions to one-dimensional p-Laplacian boundary value problems on ti
Existence and multiplicity of solutions for fourth-order boundary value problems with three paramete
Traveling fronts in diffusive and cooperative Lotka-Volterra system with nonlocal delays
Periodic solutions for dynamic equations on time scales
Permanence in delayed ratio-dependent predator-prey models with monotonic functional responses
Periodic solutions in a delayed predator-prey models with nonmonotonic functional response
Existence and global attractivity of positive periodic solutions for the impulsive delay Nicholson's
Positive solutions for second-order m-point boundary value problems on time scales
Periodic solutions of delayed predator-prey model with the Beddington-DeAngelis functional response
On the diffusive Nicholson’s blowflies equation with nonlocal delays
Existence and multiplicity of solutions for fourth-order boundary value problems with parameters
Existence of positive periodic solution of a neutral impulsive delay predator-prey system
Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonl
具有阶段结构的Lotka-Volterra合作系统的稳定性和行波解
一类不连续系统Φ-有界变差解的唯一性
Global asymptotic stability for Hopfield-type neural networks with diffusion effects
一类测度微分方程的有界变差解
偶数阶三点边值问题的多个对称正解
反正切函数的Hermite插值型多项式逼近
一类非线性项变号的奇异P—Laplacian动力方程正解的存在性
获奖
非线性泛函微分方程理论及应用
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