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高阶线性差分算子的谱结构及相应非线性问题解的分歧
  • 项目名称：高阶线性差分算子的谱结构及相应非线性问题解的分歧
  • 项目类别：地区科学基金项目
  • 批准号：11061030
  • 申请代码：A0107
  • 项目来源：国家自然科学基金
  • 研究期限：2011-01-01-2013-12-31
  • 项目负责人：马如云
  • 负责人职称：教授
  • 依托单位：西北师范大学
  • 批准年度：2010
中文摘要：

本项目拟较为系统地研究由多种边界条件所界定的差分算子的谱结构及其相应的非线性问题解的全局分歧行为。具体地，研究 Elias关于常微分算子理论的离散化；揭示高阶差分方程特征值问题的谱结构；探究二阶差分方程边值问题的类Fu?ík谱；建立二阶p-Laplacian差分方程周期边值问题的谱理论。特别在权函数变号的前提下，揭示二阶及高阶差分方程特征值问题的谱结构。给出二阶线性方程周期边值问题的Green函数为正的最优充分条件，探讨相应非线性问题正解分支的全局行为。研究非线性高阶差分方程边值问题解的全局分歧结构，推出广义简单零点解的存在性和多解性；给出含参数非线性差分方程边值问题的解集为流形的具体条件、估计解集流形的维数；特别地，当解集流形的维数为1时，推出解的唯一性以及解的确切个数。本项目的成果不仅会加深人们对许多源于实际的离散模型的理解，而且会对微分方程数值求解提供有力的理论指导。

中文主题词： 高阶差分；谱；分歧现象；广义简单零点解；变号权问题
英文摘要：

higher order difference；spectrum；bifurcation；generalinzed zeros solutions；indefinite weight problems

英文主题词： higher order difference；spectrum；bifurcation；generalinzed zeros solutions；indefinite weight problems
结论摘要：

本项目较为系统地研究由多种边界条件所界定的差分算子的谱结构及其相应的非线性问题解的全局分歧行为。具体地，研究 Elias关于常微分算子理论的离散化；揭示高阶差分方程特征值问题的谱结构；探究二阶差分方程边值问题的类Fucík谱；建立二阶p-Laplacian差分方程周期边值问题的谱理论。特别在权函数变号的前提下，揭示二阶及高阶差分方程特征值问题的谱结构。给出二阶线性方程周期边值问题的Green函数为正的最优充分条件，探讨相应非线性问题正解分支的全局行为。研究非线性高阶差分方程边值问题解的全局分歧结构，推出广义简单零点解的存在性和多解性。本项目的成果不仅会加深人们对许多源于实际的离散模型的理解，而且会对微分方程数值求解提供有力的理论指导。

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  • 期刊论文
  • 会议论文
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期刊论文
Positive periodic solutions of first-order delay differential equations with impulses
Spectrum of a linear fourth-order differential operator and its applications
Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight
Existence of Positive Solutions of Fourth-Order Problems with Integral Boundary Conditions
Stepanov-like almost automorphy for stochastic processes and applications to stochastic differential
Existence of positive periodic solutions of nonlinear first-order delayed differential equations
Global bifurcation, Berestycki's conjecture and one-sign solutions for p-Laplacian
EIGENVALUES, BIFURCATION AND ONE-SIGN SOLUTIONS FOR THE PERIODIC p-LAPLACIAN
Existence of solutions for a differential inclusion problem with singular coefficients involving the
Existence and multiplicity of positive solutions for a class of p ( x )-Kirchhoff type equations
Global structure of positive solutions for superlinear second-order periodic boundary value problems
Second order periodic problems in the presence of dry friction
Global structure of positive solutions for superlinear discrete boundary value problems
Infinitely many solutions to superlinear second order m-point boundary value problems
Existence of positive solutions for first order discrete periodic boundary value problems with delay
Positive periodic solutions of delayed differential equations
Three solutions for a nonlocal Dirichlet boundary value problem involving the p(x)-Laplacian
Existence of positive solutions for integral equations with vanishing kernels
Reverse-Order Lower and Upper Functions for Periodic Problems of Second-Order Singular Difference Eq
Global bifurcation and nodal solutions for a Sturm Liouville problem with a nonsmooth nonlinearity
Sign-changing solutions of second order dirichlet problem with impulse effects
One-Signed Periodic Solutions of First-Order Functional Differential Equations with a Parameter
Global Structure of Positive Solutions of a Discrete Problem with Sign-Changing Weight
Nonlinear periodic boundary value problems with sign-changing Green's function
Global bifurcation of positive solutions of a second-order periodic boundary value problem with inde
Periodic solutions of nonlocal semilinear fourth-order differential equations
On linear and nonlinear fourth-order eigenvalue problems with indefinite weight
Bifurcation of positive solutions of a nonlinear discrete fourth-order boundary value problem
Almost Periodic Solutions to a Stochastic Differential Equation in Hilbert Spaces
Positive Solutions of the One-Dimensional p-Laplacian with Nonlinearity Defined on a Finite Interval
Global bifurcation and nodal solutions for a Sturm-Liouville problem with a nonsmooth nonlinearity
无穷远分歧的离散周期边值问题的多个解(英文)
On positive periodic solutions of second-order difference equations with attractive-repulsive singul
Positive solutions of the second-order differential systems in reactor dynamics
二阶常微分方程Neumann边值问题正解的全局分歧
一类二阶不定权特征值问题结点解的全局结构
Solutions for a p(x)-Kirchhoff type equation with Neumann boundary data
Bifurcation from infinity and nodal solutions of quasilinear problems without the signum condition
Bifurcation of positive periodic solutions of first-order impulsive differential equations
Existence of one-signed solutions of nonlinear four-point boundary value problems
Nodal solutions of second-order two-point boundary value problems
Nodal solutions of a nonlinear eigenvalue problem of the Euler-Bernoulli equation
Positive periodic solutions of first-order singular systems
Existence and multiplicity of positive solutions of a nonlinear discrete fourth-order boundary value
Existence and multiplicity of positive solutions for a class of p(x)-Kirchhoff type equations
Existence of positive solutions to discrete second-order boundary value problems with indefinite wei
Bifurcation interval for positive solutions to discrete second-order boundary value problems
On positive solutions to equations involving the one-dimensional p-Laplacian
Global bifurcation of positive radial solutions for an elliptic system in reactor dynamics
Nodal Solutions of the p-Laplacian with Sign-Changing Weight
Unilateral global bifurcation phenomena and nodal solutions for p-Laplacian
Existence of one-signed solutions of discrete second-order periodic boundary value problems
非线性Neumann问题正解的存在性
带非齐次边界条件的p—Laplacian方程正解的存在唯一性
高阶非局部奇异半正边值问题正解的存在性问题
一类带有积分边界条件的非线性二阶边值问题正解的存在性
基数约束的投资组合优化问题的遗传算法及实证分析
一类投资优化模型的遗传算法
渐近线性二阶半正离散边值问题正解的分歧结构
一个带中转和直销的多产品运输问题及其遗传算法
一类三阶三点边值问题正解的存在性和不存在性
一类二阶非线性特征值问题的可解性
一类二阶非线性四点边值问题正解的存在唯一性
一类四阶四点边值问题正解的存在性和不存在性
EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO NONLINEAR SEMIPOSITONE NEUMANN BOUNDARY VALUE PROBLEM
一类偏差分方程的振动性
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