一类具交错扩散的强耦合退化抛物方程组解的整体存在与非存在性

本文研究了一类具交错扩散的强耦合拟线性退化抛物方程组初边值问题正古典解的局部存在,整体存在与非整体存在性.利用正则化方法和先验估计技巧证明了该问题正古典解的局部存在性,并且分别给出了该问题是否存在整体古典解的充分条件.结果表明当种群内竞争强于种群间互惠作用时,此问题存在整体解;而当两种群具有强互惠作用时,所有解都是非整体的.     

一类奇异拟线性椭圆型方程组的可解性

研究了一类P-Laplacian方程组边值问题正径向整体解的存在性和唯一性.首先,利用隐函数定理证明了该问题的局部解的存在性与唯一性,以及解对初值的连续依赖性.最后,证明了该问题存在唯一的正径向整体解.     

一类多重非线性抛物方程组解的整体不存在性

本文研究了一类多重非线性抛物方程组初边值问题解的整体不存在性,利用修正的能量扰动法,得到了正初始能量解的整体不存在性结果.     

带比例功能反应函数食物链交错扩散模型的整体解

本文研究了带有比例功能反应函数食物链交错扩散模型整体解的存在性和正平衡点的稳定性.利用能量方法和Gagliardo-Nirenberg型不等式,获得了该模型整体解的存在性和一致有界性,同时通过构造Lyapunov函数给出了该模型正平衡点全局渐近稳定的充分条件.     

带比例功能反应函数食物链交错扩散模型的整体解（英文）

本文研究了带有比例功能反应函数食物链交错扩散模型整体解的存在性和正平衡点的稳定性.利用能量方法和Gagliardo-Nirenberg型不等式,获得了该模型整体解的存在性和一致有界性,同时通过构造Lyapunov函数给出了该模型正平衡点全局渐近稳定的充分条件.     

拟线性椭圆型议程组正整体解的存在性

本文讨论了一类满足初值条件的非线性椭圆型方程组正整体解的存在性.     

高校应用数学学报第18卷 (2003年)B辑(英文版 )第1期目次和提要

具有功能反应的两斑块扩散时滞竞争系统正周期解的存在性李必文　曾宪武 (武汉大学数学与统计学院 )利用重合度连续性定理得到了具有功能反应的两斑块扩散时滞竞争系统的正周期解存在性的充分条件 .广义 Benjamin-Bona-Mahony方程 Fourier谱方法的大时间误差估计尚亚东　郭柏灵 (北京应用物理与计算数学研究所计算物理实验室 )用谱方法分析广义的 Benjamin-Bona-Mahony方程 .首先证明了该方程整体光滑解的存在性和惟一性 ,然后获得了谱逼近解和精确解的大时间误差估计 .一个耦合系统自由边界问题的整体古典解王晓华 (苏州大学数学系 )　…     

二维空间中广义Davey-Stewartson系统整体解存在的最佳条件

根据基态的特征 ,首先在二维空间中导出了广义Davey Stewartson系统解爆破和整体存在的最佳条件 ;其次得到了整体解存在的一个最佳充分条件 ;最后证明了当初值为多小时 ,该系统的整体解存在 .     

随机泛函微分方程正整体解的存在唯一性及矩有界性

构造了Lyapunov函数V (x),然后给出一个一般条件,应用Khasminskii?Mao定理,得到非线性随机泛函微分方程(SFDEs)存在正整体解,且这个解p阶矩有界.     

一类带非线性边界条件的非线性抛物方程的解的整体存在性

该文考虑带非线性边界条件的非线性抛物方程的正整体解的存在性与非存在性。通过使用上下解技巧，得到了所有正解整体存在的充分必要条件。作者所构造的上下解具有相同的形式且计算简便。     

Four positive solutions for a semilinear elliptic equation involving concave and convex nonlinearities

In this paper, we study the combined effect of concave and convex nonlinearities on the number of positive solutions for a semilinear elliptic equation. With the help of the Nehari manifold and the center mass function, we prove that there are at least four positive solutions for a semilinear elliptic equation in a finite strip with a hole.     

Multiplicity of positive solutions for semilinear elliptic problems in unbounded domains

In this paper, we study the effect of domain shape on the multiplicity of positive solutions for the semilinear elliptic equations. We prove a Palais-Smale condition in unbounded domains and assert that the semilinear elliptic equation in unbounded domains has multiple positive solutions.     

Uniqueness of the ground state solutions of quasilinear Schrödinger equations

We are concerned with the uniqueness result of positive solutions for a class of quasilinear elliptic equation arising from plasma physics. We convert a quasilinear elliptic equation into a semilinear one and show the unique existence of positive radial solution for original equation under the suitable conditions on the power of nonlinearity and quasilinearity. We also investigate the non-degeneracy of a positive radial solution for a converted semilinear elliptic equation.     

Global asymptotic behavior of solutions of a semilinear parabolic equation

We study the large time behavior of solutions for the semilinear parabolic equation . Under a general and natural condition on and the initial value , we show that global positive solutions of the parabolic equation converge pointwise to positive solutions of the corresponding elliptic equation. As a corollary of this, we recapture the global existence results on semilinear elliptic equations obtained by Kenig and Ni and by F.H. Lin and Z. Zhao. Our method depends on newly found global bounds for fundamental solutions of certain linear parabolic equations.

     

半线性椭圆方程的多解存在性

本文考虑具有凹凸非线性和临界Sobolev指数的半线性椭圆方程的正解和多重解（可能非正）的存在性。     

Global solution curves for a class of elliptic systems

We study curves of positive solutions for a system of elliptic equations of Hamiltonian type on a unit ball. We give conditions for all positive solutions to lie on global solution curves, allowing us to use the analysis similar to the case of one equation, as developed in P. Korman, Y. Li and T. Ouyang [An exact multiplicity result for a class of semilinear equations, Commun. PDE 22 (1997), pp. 661–684.] (see also T. Ouyang and J. Shi [Exact multiplicity of positive solutions for a class of semilinear problems, II, J. Diff. Eqns. 158(1) (1999), pp. 94–151].). As an application, we obtain some non-degeneracy and uniqueness results. For the one-dimensional case we also prove the positivity for the linearized problem, resulting in more detailed results.     

Exact multiplicity and global structure of solutions for a class of semilinear elliptic equations

In this paper, we establish an exact multiplicity result of solutions for a class of semilinear elliptic equation. We also obtain a precise global bifurcation diagram of the solution set. As a result, an open problem presented by C.-H. Hsu and Y.-W. Shih [C.-H. Hsu, Y.-W. Shih, Solutions of semilinear elliptic equations with asymptotic linear nonlinearity, Nonlinear Anal. 50 (2002) 275-283] is completely solved. Our argument is mainly based on bifurcation theory and continuation method.     

Existence and nonexistence of global solutions of the cauchy problem for semilinear hyperbolic equations with dissipation and with anisotropic elliptic part

We consider the Cauchy problem for a semilinear hyperbolic equation with anisotropic elliptic part and with dissipation. We prove existence and nonexistence theorems for global solutions.     

关于猝灭问题的一些结果及其应用

本文研究一类含奇异项的半线性抛物方程的初边值问题,给出了该问题的古典解整体存在或发生猝灭现象的判据以及猝灭解的生命跨度估计。同时,还用上述结果研究了一类含超Sobolev临界指标的半线性椭圆方程的Dirichlet边值问题,获得了正解的存在性结果。     

Existence of positive solutions for a class of semilinear and quasilinear elliptic equations with supercritical case

In this paper, we consider a class of semilinear elliptic Dirichlet problems in a bounded regular domain with cylindrical symmetry involving concave-convex nonlinearities with supercritical growth. Using a new Sobolev embedding theorem and variational method, we show the existence of two positive solutions of the problem. Additionally, we study the quasilinear elliptic equation and obtain a similar result.