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非线性泛函分析在流体动力学与量子力学中的应用
  • 项目名称：非线性泛函分析在流体动力学与量子力学中的应用
  • 项目类别：面上项目
  • 批准号：10871096
  • 申请代码：A0108
  • 项目来源：国家自然科学基金
  • 研究期限：2009-01-01-2011-12-31
  • 项目负责人：张吉慧
  • 负责人职称：教授
  • 依托单位：南京师范大学
  • 批准年度：2008
中文摘要：

本项目主要应用非线性泛函的工具和方法(包括变分理论和拓扑度理论等)研究流体动力学与量子力学中的某些非线性偏微分方程, 这些方程不但具有强烈的物理背景和应用背景, 而且在数学理论上也具有重要的意义。该类方程与拟线性混合型方程, 拟线性退化椭圆型方程和势函数趋于零的非线性Schrodinger 方程密切相关。 基于前人和我们过去的工作, 我们开展该类非线性偏微分方程的探索和研究。本项目致力解决如下问题:用变分理论和拓扑度理论等研究势函数趋于零的非线性Schrodinger方程解的存在性和解的能量集中问题, 通过Morse理论，收缩性及不变集等理论，获得非线性边值问题解的存在性和多解性情况。用变分理论结合二阶混合型方程的基本理论和方法探索管道流中的连续跨音速流现象, 研究非线性Tricomi 方程等混合型方程解的存在性和正则性及解的奇性传播性质。

中文主题词： 变分方法; 拟线性混合方程; 非线性Schrodinger 方程; 连续跨音速流; 非线性四阶方程
结论摘要：

英文主题词variational methods;quasilinear mixed -type equation;nonlinear Schrodinger equation;continuous transonic flow;nonlinear fourth order equation

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
  • 69
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  • 0
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期刊论文
Periodic solutions of a class of second order non-autonomous Hamiltonian systems
Positive solutions of higher-order four-point boundary value problem with p-Laplacian operator
Multiplicity of solutions for a class of elliptic systems with critical Sobolev exponent
Existence of solutions for some fourth-order nonlinear elliptic problems
The existence of three positive solutions of m-point boundary value problems for some dynamic equati
Positive Solutions for Singular Third-Order Boundary Value Problem with Dependence on the First Orde
Existence of multiple positive solutions of nth-order m-point boundary value problems
On the nonexistence of a global nontrivial subsonic solution in a 3D unbounded angular domain
On the existence and stability of a global subsonic flow in a 3D infinitely long cylindrical nozzle
EXISTENCE AND CONCENTRATION OF BOUND STATES OF NONLINEAR SCHRODINGER EQUATIONS WITH COMPACTLY SUPPOR
On transonic shocks in a conic divergent nozzle with axi-symmetric exit pressures
LOCAL STRUCTURAL STABILITY OF A MULTIDIMENSIONAL CENTERED RAREFACTION WAVE FOR THE THREE-DIMENSIONAL
Impulsive anti-periodic boundary value problem of first-order integro-differential equations
Nontrivial solutions of a class of nonlocal problems via local linking theory
Existence of three positive solutions of three-order with m-point impulsive boundary value problems
Multiplicity of solutions for a class of quasilinear elliptic equation involving the critical Sobole
Three solutions for a perturbed Dirichlet boundary value problem involving the p-Laplacian
THE EXISTENCE AND MONOTONICITY OF A THREE-DIMENSIONAL TRANSONIC SHOCK IN A FINITE NOZZLE WITH AXISYM
Existence of multiple positive solutions for third-order boundary-value problem on the half-line wit
Existence and multiple solutions for a nonlinear system with a parameter
Existence of countably many positive solutions of nth-order m-point boundary value problems
The existence of countably many positive solutions for nonlinear singular m-point boundary value pro
On Transonic Shocks in a Nozzle with Variable End Pressures
A FREE BOUNDARY VALUE PROBLEM FOR THE FULL EULER SYSTEM AND 2-D TRANSONIC SHOCK IN A LARGE VARIABLE
Bound states of nonlinear Schrodinger equations with potentials tending to zero at infinity
Global supersonic conic shock wave for the steady supersonic flow past a cone: Polytropic gas
GLOBAL MULTIDIMENSIONAL TRANSONIC CONIC SHOCK WAVE FOR THE PERTURBED SUPERSONIC FLOW PAST A CONE
Periodic solutions of non-autonomous second order systems with p-laplacin
Existence of solutions for some discrete boundary value problems with a parameter
The existence of multiple positive solutions for multi-point boundary value problems on the half-lin
Existence of positive solutions for quasilinear elliptic systems involving the p-laplacian
Existence of infinitely many mountain pass solutions for some fourth-order boundary value problems w
Positive solutions for boundary value problems of nonlinear fractional differential equation
Positive and negative solutions of a class of nonlocal problems
Existence of solutions for fourth-order boundary value problem with parameter
Infinitely many small solutions for the p&q-Laplacian problem with critical sobolev and hardy ex
The method of lower and upper solutions for 2nth-order multi-point boundary value problems
The existence of countably many positive solutions for some nonlinear singular three-point impulsive
Infinitely many mountain pass solutions on a kind of fourth-order Neumann boundary value problem
Nontrivial solutions for some fourth order boundary value problems with parameters
The existence of three positive solutions for some nonlinear boundary value problems on the half-lin
The existence of countably many positive solutions for some nonlinear three-point boundary problems
Existence of three positive solutions of m-point boundary value problems for some nonlinear fraction
Existence of traveling wavefronts of discrete reaction-diffusion equations with delay
Existence of multiple positive solutions for m-point fractional boundary value problems on an infini
Existence and uniqueness of positive solutions to m-point boundary value problem for nonlinear fract
Multiplicity of positive solutions for a semilinear p-Laplacian system with Sobolev critical exponen
Multiplicity of Solutions for Elliptic System Involving Supercritical Sobolev Exponent
Existence and uniqueness of strictly nondecreasing and positive solution for a fractional three-poin
Existence of positive entire solutions of a semilinear p–laplacian problem with a gradient ter
SOLUTIONS OF PERTURBED SCHRODINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND CRITICAL NONLINEARITY
Existence of two solutions for a navier boundary value problem involving the p-biharmonic
Periodic solutions for nonautonomous second order Hamiltonnian systems with sublinear nonlinearity
Multiplicity of solutions for quasilinear lliptic equations with critical exponential growth
MULTIPLICITY OF SOLUTIONS FOR THE NONLINEAR SCHRODINGER-MAXWELL SYSTEM
Periodic solutions of non-autonomous second order Hamiltonian systems with p-Laplacian
Multiplicity of positive solutions for a navier boundary-value problem involving the p-biharmonic wi
Existence results for a class of nonlocal problems involving p-Laplacian
带有参数的某四阶边值问题解的存在性
Orlicz-Sobolev空间上对称及非对称拟线性椭圆方程的多解性
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